HP 39gs Graphing Calculator User's Guide

HP 39gs English.book Page i Wednesday, December 7, 2005 11:24 PM

HP 39gs graphing calculator

user's guide

Edition3

Part Number F2223AA-90001

title.fm Page ii Thursday, July 13, 2006 10:29 AM

Notice

REGISTER YOUR PRODUCT AT: www.register.hp.com

THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE

PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT

NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WAR-

RANTY OF ANY KIND WITH REGARD TO THIS MANUAL,

INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES

OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS

FOR A PARTICULAR PURPOSE.

HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY

ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES

IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR

USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.

© 1994-1995, 1999-2000, 2003, 2006 Hewlett-Packard Development

Company, L.P.

Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws.

Hewlett-Packard Company

16399 West Bernardo Drive

MS 8-600

San Diego, CA 92127-1899

USA

Printing History

Edition 2

Edition 3

December 2003

June 2005

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Contents

Preface

Manual conventions .............................................................. P-1

Notice ................................................................................. P-2

1 Getting started

On/off, cancel operations......................................................1-1

The display ..........................................................................1-2

The keyboard .......................................................................1-3

Menus .................................................................................1-8

Input forms ...........................................................................1-9

Mode settings .....................................................................1-10

Setting a mode...............................................................1-11

Aplets (E-lessons).................................................................1-12

Aplet library ..................................................................1-16

Aplet views....................................................................1-16

Aplet view configuration..................................................1-18

Mathematical calculations ....................................................1-19

Using fractions....................................................................1-25

Complex numbers ...............................................................1-29

Catalogs and editors ...........................................................1-30

2 Aplets and their views

Aplet views ..........................................................................2-1

About the Symbolic view ...................................................2-1

Defining an expression (Symbolic view) ..............................2-1

Evaluating expressions ......................................................2-3

About the Plot view...........................................................2-5

Setting up the plot (Plot view setup).....................................2-5

Exploring the graph ..........................................................2-7

Other views for scaling and splitting the graph ..................2-13

About the numeric view...................................................2-16

Setting up the table (Numeric view setup) ..........................2-16

Exploring the table of numbers .........................................2-17

Building your own table of numbers..................................2-19

“Build Your Own” menu keys...........................................2-20

Example: plotting a circle ................................................2-20 i

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3 Function aplet

About the Function aplet........................................................ 3-1

Getting started with the Function aplet ................................ 3-1

Function aplet interactive analysis........................................... 3-9

Plotting a piecewise-defined function ................................ 3-12

4 Parametric aplet

About the Parametric aplet .................................................... 4-1

Getting started with the Parametric aplet............................. 4-1

5 Polar aplet

Getting started with the Polar aplet ......................................... 5-1

6 Sequence aplet

About the Sequence aplet...................................................... 6-1

Getting started with the Sequence aplet .............................. 6-1

7 Solve aplet

About the Solve aplet............................................................ 7-1

Getting started with the Solve aplet .................................... 7-2

Use an initial guess............................................................... 7-5

Interpreting results ................................................................ 7-6

Plotting to find guesses .......................................................... 7-7

Using variables in equations ................................................ 7-10

8 Linear Solver aplet

About the Linear Solver aplet ................................................. 8-1

Getting started with the Linear Solver aplet.......................... 8-1

9 Triangle Solve aplet

About the Triangle Solver aplet .............................................. 9-1

Getting started with the Triangle Solver aplet....................... 9-1

10 Statistics aplet

About the Statistics aplet...................................................... 10-1

Getting started with the Statistics aplet.............................. 10-1

Entering and editing statistical data ...................................... 10-6

Defining a regression model.......................................... 10-12

Computed statistics ........................................................... 10-14

Plotting............................................................................ 10-15

Plot types .................................................................... 10-16

Fitting a curve to 2VAR data ......................................... 10-17

Setting up the plot (Plot setup view) ................................ 10-18

Trouble-shooting a plot ................................................. 10-19 ii

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Exploring the graph ......................................................10-19

Calculating predicted values ..........................................10-20

11 Inference aplet

About the Inference aplet .....................................................11-1

Getting started with the Inference aplet .............................11-1

Importing sample statistics from the Statistics aplet ..............11-4

Hypothesis tests ..................................................................11-8

One-Sample Z-Test..........................................................11-8

Two-Sample Z-Test ..........................................................11-9

One-Proportion Z-Test....................................................11-10

Two-Proportion Z-Test ....................................................11-11

One-Sample T-Test ........................................................11-12

Two-Sample T-Test ........................................................11-14

Confidence intervals..........................................................11-15

One-Sample Z-Interval...................................................11-15

Two-Sample Z-Interval ...................................................11-16

One-Proportion Z-Interval...............................................11-17

Two-Proportion Z-Interval ...............................................11-17

One-Sample T-Interval ...................................................11-18

Two-Sample T-Interval....................................................11-19

12 Using the Finance Solver

Background........................................................................12-1

Performing TVM calculations ................................................12-4

Calculating Amortizations................................................12-7

13 Using mathematical functions

Math functions ....................................................................13-1

The MATH menu ............................................................13-1

Math functions by category ..................................................13-2

Keyboard functions.........................................................13-3

Calculus functions...........................................................13-6

Complex number functions...............................................13-7

Constants ......................................................................13-8

Conversions...................................................................13-8

Hyperbolic trigonometry..................................................13-9

List functions ................................................................13-10

Loop functions ..............................................................13-10

Matrix functions ...........................................................13-11

Polynomial functions .....................................................13-11

Probability functions......................................................13-12

Real-number functions ...................................................13-13 iii

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Two-variable statistics ................................................... 13-17

Symbolic functions ....................................................... 13-17

Test functions............................................................... 13-18

Trigonometry functions.................................................. 13-19

Symbolic calculations........................................................ 13-20

Finding derivatives ....................................................... 13-21

Program constants and physical constants ........................... 13-24

Program constants........................................................ 13-24

Physical constants ........................................................ 13-25

14 Variables and memory management

Introduction ....................................................................... 14-1

Storing and recalling variables............................................. 14-2

The VARS menu.................................................................. 14-4

Memory Manager .............................................................. 14-9

15 Matrices

Introduction ....................................................................... 15-1

Creating and storing matrices .............................................. 15-2

Working with matrices ........................................................ 15-4

Matrix arithmetic ................................................................ 15-6

Solving systems of linear equations .................................. 15-8

Matrix functions and commands ......................................... 15-10

Argument conventions .................................................. 15-10

Matrix functions ........................................................... 15-10

Examples......................................................................... 15-13

16 Lists

Displaying and editing lists .................................................. 16-4

Deleting lists.................................................................. 16-6

Transmitting lists............................................................. 16-6

List functions....................................................................... 16-6

Finding statistical values for list elements................................ 16-9

17 Notes and sketches

Introduction ....................................................................... 17-1

Aplet note view .................................................................. 17-1

Aplet sketch view................................................................ 17-3

The notepad ...................................................................... 17-6

18 Programming

Introduction ....................................................................... 18-1

Program catalog ............................................................ 18-2

Creating and editing programs ............................................ 18-4 iv

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Using programs ..................................................................18-7

Customizing an aplet...........................................................18-9

Aplet naming convention ...............................................18-10

Example ......................................................................18-10

Programming commands....................................................18-13

Aplet commands ..........................................................18-14

Branch commands ........................................................18-17

Drawing commands......................................................18-19

Graphic commands ......................................................18-21

Loop commands ...........................................................18-23

Matrix commands.........................................................18-24

Print commands............................................................18-26

Prompt commands ........................................................18-26

Stat-One and Stat-Two commands ..................................18-30

Stat-Two commands ......................................................18-30

Storing and retrieving variables in programs....................18-31

Plot-view variables ........................................................18-32

Symbolic-view variables ................................................18-39

Numeric-view variables .................................................18-41

Note variables .............................................................18-44

Sketch variables ...........................................................18-44

19 Extending aplets

Creating new aplets based on existing aplets .........................19-1

Using a customized aplet ................................................19-3

Resetting an aplet................................................................19-3

Annotating an aplet with notes .............................................19-4

Annotating an aplet with sketches .........................................19-4

Downloading e-lessons from the web.....................................19-4

Sending and receiving aplets ...............................................19-4

Sorting items in the aplet library menu list ..............................19-6

Reference information

Glossary .............................................................................. R-1

Resetting the HP 39gs............................................................ R-3

To erase all memory and reset defaults................................ R-3

If the calculator does not turn on......................................... R-4

Operating details..................................................................R-4

Batteries .......................................................................... R-4

Variables ............................................................................. R-6

Home variables................................................................ R-6

Function aplet variables.....................................................R-7

Parametric aplet variables ................................................. R-8 v

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Polar aplet variables ........................................................ R-9

Sequence aplet variables ................................................ R-10

Solve aplet variables ...................................................... R-11

Statistics aplet variables.................................................. R-12

MATH menu categories....................................................... R-13

Math functions............................................................... R-13

Program constants.......................................................... R-15

Physical Constants ......................................................... R-16

Program commands ....................................................... R-17

Status messages ................................................................. R-18

Limited Warranty

Service ..........................................................................W-3

Regulatory information.....................................................W-5

Index

vi

HP 39gs English.book Page 1 Wednesday, December 7, 2005 11:24 PM

Preface

The HP 39gs is a feature-rich graphing calculator. It is also a powerful mathematics learning tool. The HP 39gs is designed so that you can use it to explore mathematical functions and their properties.

You can get more information on the HP 39gs from

Hewlett-Packard’s Calculators web site. You can download customized aplets from the web site and load them onto your calculator. Customized aplets are special applications developed to perform certain functions, and to demonstrate mathematical concepts.

Hewlett Packard’s Calculators web site can be found at: http://www.hp.com/calculators

Manual conventions

The following conventions are used in this manual to represent the keys that you press and the menu options that you choose to perform the described operations.

• Key presses are represented as follows:

• Shift keys, that is the key functions that you access by pressing the key first, are represented as follows:

CLEAR

,

MODES

,

ACOS , etc.

• Numbers and letters are represented normally, as follows:

5, 7, A, B, etc.

• Menu options, that is, the functions that you select using the menu keys at the top of the keypad are represented as follows:

, , .

• Input form fields and choose list items are represented as follows:

Function, Polar, Parametric

• Your entries as they appear on the command line or within input forms are represented as follows:

2*X

2

-3X+5

P-1

Preface.fm Page 2 Thursday, July 13, 2006 10:33 AM

Notice

This manual and any examples contained herein are provided as-is and are subject to change without notice.

Except to the extent prohibited by law, Hewlett-Packard

Company makes no express or implied warranty of any kind with regard to this manual and specifically disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-Packard

Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein.

© 1994–1995, 1999–2000, 2003–2006 Hewlett-

Packard Development Company, L.P.

The programs that control your HP 39gs are copyrighted and all rights are reserved. Reproduction, adaptation, or translation of those programs without prior written permission from Hewlett-Packard Company is also prohibited.

P-2


1

Getting started

On/off, cancel operations

To turn on

To cancel

To turn off

HOME

Protective cover

Press to turn on the calculator.

When the calculator is on, the current operation.

key cancels the

Press OFF to turn the calculator off.

To save power, the calculator turns itself off after several minutes of inactivity. All stored and displayed information is saved.

If you see the ((•)) annunciator or the Low Bat message, then the calculator needs fresh batteries.

HOME is the calculator’s home view and is common to all aplets. If you want to perform calculations, or you want to quit the current activity (such as an aplet, a program, or an editor), press . All mathematical functions are available in the HOME. The name of the current aplet is displayed in the title of the home view.

The calculator is provided with a slide cover to protect the display and keyboard. Remove the cover by grasping both sides of it and pulling down.

You can reverse the slide cover and slide it onto the back of the calculator. this will help prevent you losing the cover while you are using the calculator.

To prolong the life of the calculator, always place the cover over the display and keyboard when you are not using the calculator.

Getting started 1-1


The display

To adjust the contrast

Simultaneously press decrease) the contrast.

and (or ) to increase (or

To clear the display

• Press CANCEL to clear the edit line.

• to clear the edit line and the display history.

Parts of the display

Title

History

Edit line

Menu key labels

N O T E

Menu key or soft key labels. The labels for the menu keys’ current meanings. is the label for the first menu key in this picture. “Press ” means to press the first menu key, that is, the leftmost top-row key on the calculator keyboard.

Edit line. The line of current entry.

History. The HOME display ( ) shows up to four lines of history: the most recent input and output. Older lines scroll off the top of the display but are retained in memory.

Title. The name of the current aplet is displayed at the top of the HOME view. RAD, GRD, DEG specify whether

Radians, Grads or Degrees angle mode is set for HOME.

The and symbols indicate whether there is more history in the HOME display. Press the and to scroll in the HOME display.

This user’s guide contains images from the HP 39gs and does not display the menu key label.

1-2 Getting started


The keyboard

Menu keys

Annunciators. Annunciators are symbols that appear above the title bar and give you important status information.

Annunciator

α

((•))

Description

Shift in effect for next keystroke.

To cancel, press again.

Alpha in effect for next keystroke.

To cancel, press again.

Low battery power.

Busy.

Data is being transferred via infrared or cable.

HP 39gs

Graphing Calculator

Menu Key

Labels

Menu Keys

Aplet Control

Keys

Cursor

Keys

Alpha Key

Shift Key

Getting started

Enter

Key

1-3


Aplet control keys

• On the calculator keyboard, the top row of keys are called menu keys. Their meanings depend on the context—that’s why their tops are blank. The menu keys are sometimes called “soft keys”.

• The bottom line of the display shows the labels for the menu keys’ current meanings.

The aplet control keys are:

Key Meaning

Displays the Symbolic view for the

current aplet. See “Symbolic view” on page 1-16.

Displays the Plot view for the current

aplet. See “Plot view” on page 1-16.

Displays the Numeric view for the

current aplet. See “Numeric view” on page 1-17.

Displays the HOME view. See

“HOME” on page 1-1.

Displays the Aplet Library menu. See

“Aplet library” on page 1-16.

Displays the VIEWS menu. See

“Aplet views” on page 1-16.

1-4 Getting started


Entry/Edit keys

The entry and edit keys are:

Key

( CANCEL

CLEAR

)

Meaning

Cancels the current operation if the calculator is on by pressing then

.

turns the calculator off.

Accesses the function printed in blue above a key.

Returns to the HOME view, for performing calculations.

Accesses the alphabetical characters printed in orange below a key. Hold down to enter a string of characters.

Enters an input or executes an operation. In calculations, acts like “=”. When or is present as a menu key, acts the same as pressing or

.

Enters a negative number. To enter

–25, press 25. Note: this is not the same operation that the subtract

button performs ( ).

Enters the independent variable by inserting X, T, θ, or N into the edit line, depending on the current active aplet.

Deletes the character under the cursor. Acts as a backspace key if the cursor is at the end of the line.

Clears all data on the screen. On a settings screen, for example Plot

returns all settings to their default values.

, , , Moves the cursor around the display. Press first to move to the beginning, end, top or bottom.

Getting started 1-5


Key

CHARS

Meaning (Continued)

Displays a menu of all available characters. To type one, use the arrow keys to highlight it, and press

. To select multiple characters, select each and press press .

, then

Shifted keystrokes

There are two shift keys that you use to access the operations and characters printed above the keys: and .

Key Description

Press the key to access the operations printed in blue above the keys. For instance, to access the

Modes screen, press , then press . is labeled in blue above the key). You do not need to hold down when you press HOME. This action is depicted in this manual as “press

MODES .”

To cancel a shift, press again.

The alphabetic keys are also shifted keystrokes. For instance, to type Z, press Z. (The letters are printed in orange to the lower right of each key.)

To cancel Alpha, press again.

For a lower case letter, press

.

For a string of letters, hold down

while typing.

1-6 Getting started


HELPWITH

Example

The HP 39gs built-in help is available in HOME only. It provides syntax help for built-in math functions.

Access the HELPWITH command by pressing

SYNTAX and then the math key for which you require syntax help.

Press SYNTAX

Math keys

Getting started

Note: Remove the left parenthesis from built-in functions such as sine, cosine, and tangent before invoking the HELPWITH command.

HOME ( ) is the place to do calculations.

Keyboard keys. The most common operations are available from the keyboard, such as the arithmetic (like

) and trigonometric (like ) functions. Press to complete the operation: displays 16.

256

.

MATH menu. Press

to open the MATH menu. The MATH menu is a comprehensive list of math functions that do not appear on the keyboard. It also includes categories for all other functions and constants.

The functions are grouped by category, ranging in alphabetical order from Calculus to Trigonometry.

• The arrow keys scroll through the list ( , ) and move from the category list in the left column to the item list in the right column ( , ).

• Press to insert the selected command onto the edit line.

• Press to dismiss the MATH menu without selecting a command.

• Pressing displays the list of Program

Constants. You can use these in programs that you develop.

1-7


Program commands

Inactive keys

H I N T

• Pressing displays a menu of physical constants from the fields of chemistry, physics, and quantum mechanics. You can use these

constants in calculations. (See “Physical constants” on page 13-25 for more information.)

• Pressing

MATH menu.

takes you to the beginning of the

See “Math functions by category” on page 13-2 for

details of the math functions.

When using the MATH menu, or any menu on the hp 39gs, pressing an alpha key takes you straight to the first menu option beginning with that alpha character.

With this method, you do not need to press first.

Just press the key that corresponds to the command’s beginning alpha character.

Commands. See “Programming commands” on page 18-13.

If you press a key that does not operate in the current context, a warning symbol like this

!

appears. There is no beep.

Menus

A menu offers you a choice of items. Menus are displayed in one or two columns.

To search a menu

• The arrow in the display means more items below.

• The arrow in the display means more items above.

• Press or to scroll through the list. If you press

or , you’ll go all the way to the end or the beginning of the list. Highlight the item you want to select, then press (or ).

1-8 Getting started


To cancel a menu

• If there are two columns, the left column shows general categories and the right column shows specific contents within a category. Highlight a general category in the left column, then highlight an item in the right column. The list in the right column changes when a different category is highlighted.

Press when you have highlighted your selection.

• To speed-search a list, type the first letter of the word.

For example, to find the Matrix category in , press , the Alpha “M” key.

• To go up a page, you can press down a page, press .

. To go

CANCEL ) or current operation.

. This cancels the

Input forms

An input form shows several fields of information for you to examine and specify. After highlighting the field to edit, you can enter or edit a number (or expression). You can also select options from a list ( ). Some input forms include items to check ( examples input forms.

). See below for

Reset input form values

To reset a field to its default values in an input form, move the cursor to that field and press . To reset all default field values in the input form, press CLEAR .

Getting started 1-9


Mode settings

H I N T

You use the Modes input form to set the modes for HOME.

Although the numeric setting in Modes affects only

HOME, the angle setting controls HOME and the current aplet. The angle setting selected in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you use the SETUP keys ( and ).

Press to access the HOME MODES input form.

Setting

Angle

Measure

Number

Format

Options

Angle values are:

Degrees. 360 degrees in a circle.

Radians. 2π radians in a circle.

Grads. 400 grads in a circle.

The angle mode you set is the angle setting used in both HOME and the current aplet. This is done to ensure that trigonometric calculations done in the current aplet and HOME give the same result.

The number format mode you set is the number format used in both HOME and the current aplet.

Standard. Full-precision display.

Fixed. Displays results rounded to a number of decimal places. Example:

123.456789 becomes 123.46 in

Fixed 2 format.

Scientific. Displays results with an exponent, one digit to the left of the decimal point, and the specified number of decimal places. Example:

123.456789 becomes 1.23E2 in

Scientific 2 format.

1-10 Getting started


Setting

Decimal

Mark

Options (Continued)

Engineering. Displays result with an exponent that is a multiple of 3, and the specified number of significant digits beyond the first one. Example:

123.456E7 becomes 1.23E9 in

Engineering 2 format.

Fraction. Displays results as fractions based on the specified number of decimal places. Examples:

123.456789 becomes 123 in

Fraction 2 format, and .333 becomes

1/3 and 0.142857 becomes 1/7.

See “Using fractions” on page 1-25.

Mixed Fraction. Displays results as mixed fractions based on the specified number of decimal places. A mixed fraction has an integer part and a fractional part. Examples:

123.456789 becomes 123+16/35 in Fraction 2 format, and 7÷ 3 returns

2+1/3. See “Using fractions” on page 1-25.

Dot or Comma. Displays a number as 12456.98 (Dot mode) or as

12456,98 (Comma mode). Dot mode uses commas to separate elements in lists and matrices, and to separate function arguments. Comma mode uses periods (dot) as separators in these contexts.

Setting a mode

This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the same for changing number format and decimal mark modes.

1. Press to open the HOME MODES input form.

Getting started 1-11


The cursor (highlight) is in the first field, Angle

Measure.

2. Press to display a list of choices.

H I N T

3. Press to select

Degrees, and press

. The angle measure changes to degrees.

4. Press

HOME.

to return to

Whenever an input form has a list of choices for a field, you can press to cycle through them instead of using

.

Aplets (E-lessons)

Aplets are the application environments where you explore different classes of mathematical operations. You select the aplet that you want to work with.

Aplets come from a variety of sources:

• Built-in the HP 39gs (initial purchase).

• Aplets created by saving existing aplets, which have been modified, with specific configurations. See

“Creating new aplets based on existing aplets” on page 19-1.

• Downloaded from HP’s Calculators web site.

• Copied from another calculator.

Aplets are stored in the Aplet

library. See “Aplet library” on page 1-16 for further

information.

You can modify configuration settings for the graphical, tabular, and



Getting started symbolic views of the aplets in the following table. See

“Aplet view configuration” on page 1-18 for further

information.

Aplet name

Function

Use this aplet to explore:

Inference

Real-valued, rectangular functions y in terms of x. Example: y = 2x

2

+ 3x 5 .

Confidence intervals and Hypothesis tests based on the Normal and

Students-t distributions.

Parametric Parametric relations x and y in terms of

t. Example: x = cos(t) and y = sin(t).

Polar Polar functions r in terms of an angle θ.

= cos 4 θ

Sequence Sequence functions U in terms of n, or in terms of previous terms in the same or another sequence, such as

U and U

. Example: n

= U +

U

1

U

= 0

.

,

U

U

2

=

and

1

Solve Equations in one or more real-valued variables. Example: = x

2

– x – 2 .

Finance

Linear

Solver

Triangle

Solver

Statistics

Time Value of Money (TVM) calculations.

Solutions to sets of two or three linear equations.

Unknown values for the lengths and angles of triangles.

One-variable (x) or two-variable (x and

y) statistical data.

In addition to these aplets, which can be used in a variety of applications, the HP 39gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configuration settings for these aplets.

A great many more teaching aplets can be found at HP’s web site and other web sites created by educators, together with accompanying documentation, often with student work sheets. These can be downloaded free of

1-13


Quad Explorer aplet

H I N T charge and transferred to the HP 39gs using the provided

Connectivity Kit.

The Quad Explorer aplet is used to investigate the behaviour of y = ( + ) + v as the values of a, h and

v change, both by manipulating the equation and seeing the change in the graph, and by manipulating the graph and seeing the change in the equation.

More detailed documentation, and an accompanying student work sheet can be found at HP’s web site.

1-14

Explorer, and then press

. The Quad Explorer aplet opens in mode, in which the arrow keys, the and keys, and the key are used to change the shape of the graph. This changing shape is reflected in the equation displayed at the top right corner of the screen, while the original graph is retained for comparison. In this mode the graph controls the equation.

It is also possible to have the equation control the graph. sub-expression of your equation.

Pressing the and key moves between subexpressions, while pressing the and key changes their values.

Pressing allows the user to select whether all three sub-expressions will be explored at once or only one at a time.

A button is provided to evaluate the student’s knowledge. Pressing displays a target quadratic graph. The student must manipulate the equation’s parameters to make the equation match the target graph. When a student feels that they have correctly chosen the parameters a button evaluates the answer and provide feedback. An

button is provided for those who give up!

Getting started


Trig Explorer aplet

The Trig Explorer aplet is used to investigate the behaviour of the graph of y = a sin ( + as the values of a, b, c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation.

Explorer, and then press

to display the screen shown right.

In this mode, the graph controls the equation.

Pressing the and

keys transforms the graph, with these transformations reflected in the equation.

The button labelled a toggle between

is

Origin is chosen, the ‘point of control’ is at the origin (0,0) and keys control vertical and horizontal transformations. When is chosen the

‘point of control’ is on the first extremum of the graph (i.e. for the sine graph at ( ⁄ , ) .

The arrow keys change the amplitude and frequency of the graph. This is most easily seen by experimenting.

Extremum

Getting started

Pressing displays the equation at the top of the screen. The equation is controlled by the graph.

Pressing the and keys moves from parameter to parameter. Pressing the or key changes the parameter’s values.

The default angle setting for this aplet is radians. The angle setting can be changed to degrees by pressing

.

1-15


Aplet library

To open an aplet

Aplets are stored in the Aplet library.

Press to display the Aplet library menu. Select the aplet and press or .

From within an aplet, you can return to HOME any time by pressing .

Aplet views

Symbolic view

Plot view

When you have configured an aplet to define the relation or data that you want to explore, you can display it in different views. Here are illustrations of the three major aplet views (Symbolic, Plot, and Numeric), the six supporting aplet views (from the VIEWS menu), and the two user-defined views (Note and Sketch).

Note: some aplets—such as the Linear Solver aplet and the Triangle Solver aplet—only have a single view, the

Numeric view.

Press to display the aplet’s Symbolic view.

You use this view to define the function(s) or equation(s) that you want to explore.

See “About the Symbolic view” on page 2-1 for

further information.

Press to display the aplet’s Plot view.

In this view, the functions that you have defined are displayed graphically.

See “About the Plot view” on page 2-5 for further

information.



Numeric view

Press to display the aplet’s Numeric view.

In this view, the functions that you have defined are displayed in tabular format.

See “About the numeric view” on page 2-16 for


Plot-Table view

The VIEWS menu contains the Plot-Table view.

Select Plot-Table

Splits the screen into the plot and the data table. See

“Other views for scaling and splitting the graph” on page 2-13 for futher information.

Plot-Detail view

The VIEWS menu contains the Plot-Detail view.

Select Plot-Detail

Splits the screen into the plot and a close-up.

See “Other views for scaling and splitting the graph” on page 2-13 for further information.

Overlay Plot view

The VIEWS menu contains the Overlay Plot view.

Select Overlay Plot

Plots the current expression(s) without erasing any pre-existing plot(s).

See “Other views for scaling and splitting the graph” on page 2-13 for further information.



Note view

Sketch view

This note is transferred with the aplet if it is sent to another calculator or to a

PC. A note view contains text to supplement an aplet.

See “Notes and sketches” on page 17-1 for further

information.

SKETCH to display the aplet’s sketch view.

Displays pictures to supplement an aplet.

See “Notes and sketches” on page 17-1 for further

information.

Aplet view configuration

You use the SETUP keys ( , and

SETUP

) to configure the aplet. For example, press

-

PLOT ( ) to display the input form for setting the aplet’s plot settings. Angle measure is controlled using the MODES view.

Plot Setup

Press PLOT .

Sets parameters to plot a graph.

Numeric Setup

Press NUM . Sets parameters for building a table of numeric values.

Symbolic Setup

This view is only available in the Statistics aplet in mode, where it plays an important role in choosing data models.

Press SYMB .



To change views

To save aplet configuration

Each view is a separate environment. To change a view, select a different view by pressing , , keys or select a view from the VIEWS menu. To change to HOME, press . You do not explicitly close the current view, you just enter another one—like passing from one room into another in a house. Data that you enter is automatically saved as you enter it.

You can save an aplet configuration that you have used, and transfer the aplet to other HP 39gs calculators. See

“Creating new aplets based on existing aplets” on page 19-1.

Mathematical calculations

The most commonly used math operations are available from the keyboard. Access to the rest of the math functions is via the MATH menu ( ).

To access programming commands, press CMDS .

See “Programming commands” on page 18-13 for


Where to start

The home base for the calculator is the HOME view

( ). You can do all calculations here, and you can access all operations.

Entering expressions

• Enter an expression into the HP 39gs in the same leftto-right order that you would write the expression.

This is called algebraic entry.

• To enter functions, select the key or MATH menu item for that function. You can also enter a function by using the Alpha keys to spell out its name.

• Press to evaluate the expression you have in the edit line (where the blinking cursor is). An

expression can contain numbers, functions, and variables.



Example

23

2

–

–

14 8

3 ln ( )

23

14

45

3

8

Long results

Negative numbers

Scientific notation

(powers of 10)

Example

If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to highlight it and then press .

Type to start a negative number or to insert a negative sign.

To raise a negative number to a power, enclose it in parentheses. For example, (–5)

2

= 25, whereas –5

2

=

–25.

A number like

4

or ×

– 7

is written in

scientific notation, that is, in terms of powers of ten. This is simpler to work with than 50000 or 0.000000321. To enter numbers like these, use EEX . (This is easier than using 10 .)

Calculate

(

– 13 23

----------------------------------------------------

– 5

)

13

6

23 3 EEX

5

Explicit and implicit multiplication

1-20

Implied multiplication takes place when two operands appear with no operator in between. If you enter AB, for example, the result is A*B.

Getting started


H I N T

However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression. It is clearest to enter AB as A*B.

Implied multiplication will not always work as expected.

For example, entering A(B+4) will not give A*(B+4).

Instead an error message is displayed: “Invalid User

Function”. This is because the calculator interprets

A(B+4) as meaning ‘evaluate function A at the value

B+4’, and function A does not exist. When in doubt, insert the * sign manually.

Parentheses

You need to use parentheses to enclose arguments for functions, such as SIN(45). You can omit the final parenthesis at the end of an edit line. The calculator inserts it automatically.

Parentheses are also important in specifying the order of operation. Without parentheses, the HP 39gs calculates according to the order of algebraic precedence (the next topic). Following are some examples using parentheses.

Entering...

45

45

π

π

85 9

85 9

Calculates...

sin (45 + π) sin (45) + π



Algebraic precedence order of evaluation

Largest and smallest numbers

Clearing numbers

Using previous results

Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right.

1. Expressions within parentheses. Nested parentheses are evaluated from inner to outer.

2. Prefix functions, such as SIN and LOG.

3. Postfix functions, such as !

4. Power function, ^, NTHROOT.

5. Negation, multiplication, and division.

6. Addition and subtraction.

7. AND and NOT.

8. OR and XOR.

9. Left argument of | (where).

10.Equals, =.

The smallest number the HP 39gs can represent is

1 × 10

–499

(1E–499). A smaller result is displayed as zero. The largest number is 9.99999999999 × 10

499

(1E499). A greater result is displayed as this number.

• clears the character under the cursor. When the cursor is positioned after the last character, deletes the character to the left of the cursor, that is, it performs the same as a backspace key.

•

CANCEL ( ) clears the edit line.

• CLEAR clears all input and output in the display, including the display history.

The HOME display ( ) shows you four lines of input/output history. An unlimited (except by memory) number of previous lines can be displayed by scrolling.

You can retrieve and reuse any of these values or expressions.

Input

Last input

Edit line

Output

Last output



When you highlight a previous input or result (by pressing

), the and menu labels appear.

To copy a previous line

To reuse the last result

Highlight the line (press ) and press . The number (or expression) is copied into the edit line.

To repeat a previous line

Example

HOME display into an expression. ANS is a variable that is updated each time you press .

To repeat the very last line, just press . Otherwise, highlight the line (press ) first, and then press .

The highlighted expression or number is re-entered. If the previous line is an expression containing the ANS , the calculation is repeated iteratively.

See how

(50), and

50

ANS retrieves and reuses the last result

updates ANS (from 50 to 75 to 100).

25

You can use the last result as the first expression in the edit line without pressing ANS . or

, (or other operators that require a preceding argument) automatically enters ANS before the operator.

You can reuse any other expression or value in the HOME display by highlighting the expression (using the arrow keys), then pressing

. See “Using previous results” on page 1-22 for more details.

The variable ANS is different from the numbers in HOME’s display history. A value in ANS is stored internally with the full precision of the calculated result, whereas the displayed numbers match the display mode.



H I N T

Storing a value in a variable

When you retrieve a number from ANS , you obtain the result to its full precision. When you retrieve a number from the HOME’s display history, you obtain exactly what was displayed.

Pressing whereas pressing into the edit line.

evaluates (or re-evaluates) the last input,

ANS copies the last result (as ANS )

You can save an answer in a variable and use the variable in later calculations. There are 27 variables available for storing real values. These are A to Z and θ.

See Chapter 14, “Variables and memory management”

for more information on variables. For example:

1. Perform a calculation.

45 8 3

2. Store the result in the A variable.

A

3. Perform another calculation using the A variable.

95 2 A



Accessing the display history

Pressing enables the highlight bar in the display history. While the highlight bar is active, the following menu and keyboard keys are very useful:

Key

,

CLEAR

Function

Scrolls through the display history.

Copies the highlighted expression to the position of the cursor in the edit line.

Displays the current expression in standard mathematical form.

Deletes the highlighted expression from the display history, unless there is a cursor in the edit line.

Clears all lines of display history and the edit line.

Clearing the display history

It’s a good habit to clear the display history (

CLEAR ) whenever you have finished working in HOME. It saves calculator memory to clear the display history.

Remember that all your previous inputs and results are saved until you clear them.

Using fractions

To work with fractions in HOME, you set the number format to Fraction or Mixed Fraction, as follows:

Setting Fraction mode

1. In HOME, open the HOME MODES input form.

MODES



2. Select Number Format, press to display the options, and highlight Fraction or Mixed

Fraction.

3. Press to select the Number Format option, then move to the precision value field.

Setting fraction precision

4. Enter the precision value that you want to use, and press to set the precision. Press to HOME.

to return

See “Setting fraction precision” below for more information.

The fraction precision setting determines the precision in which the HP 39gs converts a decimal value to a fraction.

The greater the precision value that is set, the closer the fraction is to the decimal value.

By choosing a precision of 1 you are saying that the fraction only has to match 0.234 to at least 1 decimal place (3/13 is 0.23076...).

The fractions used are found using the technique of continued fractions.

When converting recurring decimals this can be important. For example, at precision 6 the decimal

0.6666 becomes 3333/5000 (6666/10000) whereas at precision 3, 0.6666 becomes 2/3, which is probably what you would want.

For example, when converting .234 to a fraction, the precision value has the following effect:



• Precision set to 1:



• Precision set to 4

Fraction calculations

Getting started

When entering fractions:

• You use the key to separate the numerator part and the denominator part of the fraction.

• To enter a mixed fraction, for example, 1

1

/

2

, you enter it in the format (1+

1

/

2

).

For example, to perform the following calculation:

3(2

3

/

4

+ 5

7

/

8

)

1. Set the Number format mode to Fraction or

Mixed Fraction and specify a precision value of

4.

In this example, we’ll select Fraction as our format.)

MODES

Select

Fraction

4

1-27


Converting decimals to fractions

2. Enter the calculation.

3

4

8

2 3

5 7

Note: Ensure you are in the HOME view.

3. Evaluate the calculation.

Note that if you had selected Mixed

Fraction instead of

Fraction as the

Number format, the answer would have been expressed as 25+7/8.

To convert a decimal value to a fraction:

1. Set the number format mode to Fraction or Mixed

Fraction.

2. Either retrieve the value from the History, or enter the value on the command line.

3. Press to convert the number to a fraction.

When converting a decimal to a fraction, keep the following points in mind:

• When converting a recurring decimal to a fraction, set the fraction precision to about 6, and ensure that you include more than six decimal places in the recurring decimal that you enter.

In this example, the fraction precision is set to 6. The top calculation returns the correct result. The bottom one does not.

• To convert an exact decimal to a fraction, set the fraction precision to at least two more than the number of decimal places in the decimal.



In this example, the fraction precision is set to 6.

Complex numbers

Complex results

To enter complex numbers

The HP 39gs can return a complex number as a result for some math functions. A complex number appears as an ordered pair (x, y), where x is the real part and y is the imaginary part. For example, entering – 1 returns (0,1).

Enter the number in either of these forms, where x is the real part, y is the imaginary part, and i is the imaginary

Storing complex numbers

• (x, y) or

• x + iy.

To enter i:

• press or

• press , keys to select Constant,

to move to the right column of the menu, to select i, and .

There are 10 variables available for storing complex numbers: Z0 to Z9. To store a complex number in a variable:

• Enter the complex number, press , enter the variable to store the number in, and press .

4 5

Z 0



Catalogs and editors

The HP 39gs has several catalogs and editors. You use them to create and manipulate objects. They access features and stored values (numbers or text or other items) that are independent of aplets.

• A catalog lists items, which you can delete or transmit, for example an aplet.

• An editor lets you create or modify items and numbers, for example a note or a matrix.

Catalog/Editor

(

Aplet library

)

(

Sketch editor

SKETCH )

Contents

Aplets.

List (

Matrix (

MATRIX )

Notepad (

NOTEPAD )

Program (

PROGRM )

LIST )

Sketches and diagrams, See

Chapter 17, “Notes and sketches”.

Lists. In HOME, lists are

enclosed in {}. See Chapter 16,

“Lists”.

One- and two-dimensional arrays. In HOME, arrays are

enclosed in []. See Chapter 15,

“Matrices”.

Notes (short text entries). See

Chapter 17, “Notes and sketches”.

Programs that you create, or associated with user-defined

aplets. See Chapter 18,

“Programming”.



2

Aplets and their views

Aplet views

This section examines the options and functionality of the three main views for the Function, Polar, Parametric, and

Sequence aplets: Symbolic, Plot, and Numeric views.

About the Symbolic view

The Symbolic view is the defining view for the Function,

Parametric, Polar, and Sequence aplets. The other views are derived from the symbolic expression.

You can create up to 10 different definitions for each

Function, Parametric, Polar, and Sequence aplet. You can graph any of the relations (in the same aplet) simultaneously by selecting them.

Defining an expression (Symbolic view)

Choose the aplet from the Aplet Library.

Aplets and their views

Press or to select an aplet.

The Function,

Parametric, Polar, and Sequence aplets start in the

Symbolic view.

(

If the highlight is on an existing expression, scroll to an empty line—unless you don’t mind writing over the expression—or, clear one line ( ) or all lines

CLEAR ).

Expressions are selected (check marked) on entry. To deselect an expression, press expressions are plotted.

. All selected

2-1


– For a Function

definition, enter an expression to define F(X). The only independent variable in the expression is X.

– For a

Parametric

definition, enter a pair of expressions to define X(T) and

Y(T). The only independent variable in the expressions is T.

– For a Polar

definition, enter an expression to define R(θ). The only independent variable in the expression is θ.

– For a Sequence

definition, either enter the first term, or the first and second terms, for U

(U1, or...U9, or

U0). Then define the nth term of the sequence in terms of N or of the prior terms, U(N–1) and/or U(N–2). The expressions should produce real-valued sequences with integer domains. Or define the

nth term as a non-recursive expression in terms of

n only. In this case, the calculator inserts the first two terms based on the expression that you define.

– Note: You will have to enter the second term if the hp39gs is unable to calculate it automatically.

Typically if Ux(N) depends on Ux(N–2) then you must enter Ux(2).

2-2 Aplets and their views


Evaluating expressions

In aplets

In the Symbolic view, a variable is a symbol only, and does not represent one specific value. To evaluate a function in Symbolic view, press . If a function calls another function, then resolves all references to other functions in terms of their independent variable.

1. Choose the Function aplet.

Select Function

2. Enter the expressions in the Function aplet’s Symbolic view.

A

B

F1

F2

3. Highlight F3(X).

4. Press

Note how the values for F1(X) and F2(X) are substituted into F3(X).

Aplets and their views 2-3


In HOME

You can also evaluate any expression in HOME by entering it into the edit line and pressing .

For example, define F4 as below. In HOME, type

F4(9)and press . This evaluates the expression, substituting 9 in place of X into F4.

SYMB view keys

The following table details the menu keys that you use to work with the Symbolic view.

Key Meaning

Copies the highlighted expression to the edit line for editing. Press when done.

Checks/unchecks the current expression (or set of expressions).

Only checked expression(s) are evaluated in the Plot and Numeric views.

Enters the independent variable in the

Function aplet. Or, you can use the

key on the keyboard.


Parametric aplet. Or, you can use the key on the keyboard.


Polar aplet. Or, you can use the



Sequence aplet. Or, you can use the


Displays the current expression in text book form.

Resolves all references to other definitions in terms of variables and evaluates all arithmetic expressions.

Displays a menu for entering variable names or contents of variables.



Key

CHARS

CLEAR


Displays the menu for entering math operations.

Displays special characters. To enter one, place the cursor on it and press

. To remain in the CHARS menu and enter another special character, press .

Deletes the highlighted expression or the current character in the edit line.

Deletes all expressions in the list or clears the edit line.

About the Plot view

After entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings.

You can plot up to ten expressions at the same time.

Select the expressions you want to be plotted together.

Setting up the plot (Plot view setup)

Press SETUP PLOT to define any of the settings shown in the next two tables.

1. Highlight the field to edit.

– If there is a number to enter, type it in and press

or .

– If there is an option to choose, press highlight your choice, and press

As a shortcut to , just highlight the field to change and press to cycle through the options.

,

or .

– If there is an option to select or deselect, press

to check or uncheck it.

2. Press to view more settings.

3. When done, press to view the new plot.



Plot view settings

2-6

The plot view settings are:

Field

XRNG, YRNG

RES

TRNG

θRNG

NRNG

TSTEP

θSTEP

SEQPLOT

Meaning

Specifies the minimum and maximum horizontal (X) and vertical (Y) values for the plotting window.

For function plots: Resolution;

“Faster” plots in alternate pixel columns; “Detail” plots in every pixel column.

Parametric aplet: Specifies the tvalues (T) for the graph.

Polar aplet: Specifies the angle (θ) value range for the graph.

Sequence aplet: Specifies the index (N) values for the graph.

For Parametric plots: the increment for the independent variable.

For Polar plots: the increment value for the independent variable.

For Sequence aplet: Stairstep or

Cobweb types.

XTICK

YTICK

Horizontal spacing for tickmarks.

Vertical spacing for tickmarks.

Those items with space for a checkmark are settings you can turn on or off. Press to display the second page.

Field

SIMULT

INV. CROSS

Meaning

If more than one relation is being plotted, plots them simultaneously

(otherwise sequentially).

Cursor crosshairs invert the status of the pixels they cover.



Field

CONNECT

LABELS

AXES

GRID


Connect the plotted points. (The

Sequence aplet always connects them.)

Label the axes with XRNG and

YRNG values.

Draw the axes.

Draw grid points using XTICK and YTICK spacing.

Reset plot settings

To reset the default values for all plot settings, press

CLEAR in the Plot Setup view. To reset the default value for a field, highlight the field, and press .

Exploring the graph

Plot view gives you a selection of keys and menu keys to explore a graph further. The options vary from aplet to aplet.

PLOT view keys

The following table details the keys that you use to work with the graph.

Key

CLEAR

Meaning

Erases the plot and axes.

Offers additional pre-defined views for splitting the screen and for scaling

(“zooming”) the axes.

Moves cursor to far left or far right.

or

Moves cursor between relations.

Interrupts plotting.

Continues plotting if interrupted.



Trace a graph

To move between relations

2-8

Key Meaning (Continued)

Turns menu-key labels on and off.

When the labels are off, pressing

turns them back on.

• Pressing once displays the full row of labels.

• Pressing a second time removes the row of labels to

• display only the graph.

Pressing a third time displays the coordinate mode.

Displays the ZOOM menu list.

Turns trace mode on/off. A white box appears over the on .

Opens an input form for you to enter an X (or T or N or θ) value. Enter the value and press . The cursor jumps to the point on the graph that you entered.

Function aplet only: turns on menu list for root-finding functions (see

“Analyse graph with FCN functions” on page 3-4).

Displays the current, defining expression. Press menu.

to restore the

You can trace along a function using the or key which moves the cursor along the graph. The display also shows the current coordinate position (x, y) of the cursor.

Trace mode and the coordinate display are automatically set when a plot is drawn.

Note: Tracing might not appear to exactly follow your plot if the resolution (in Plot Setup view) is set to Faster.

This is because RES: FASTER plots in only every other column, whereas tracing always uses every column.

In Function and Sequence Aplets: You can also scroll (move the cursor) left or right beyond the edge of the display window in trace mode, giving you a view of more of the plot.

If there is more than one relation displayed, press or

to move between relations.



To jump directly to a value

To jump straight to a value rather than using the Trace function, use the menu key. Press , then enter a value. Press to jump to the value.

To turn trace on/off

If the menu labels are not displayed, press

• Turn off trace mode by pressing

• Turn on trace mode by pressing

• To turn the coordinate display off, press

.

.

first.

.

Zoom within a graph

One of the menu key options is . Zooming redraws the plot on a larger or smaller scale. It is a shortcut for changing the Plot Setup.

The Set Factors... option enables you to set the factors by which you zoom in or zoom out, and whether the zoom is centered about the cursor.

ZOOM options

Press , select an option, and press . (If is not displayed, press .) Not all options are available in all aplets.

Option

Center

Box...

In

Meaning

Re-centers the plot around the current position of the cursor without changing the scale.

Lets you draw a box to zoom in on.

See “Other views for scaling and splitting the graph” on page 2-13.

Divides horizontal and vertical scales by the X-factor and Y-factor.

For instance, if zoom factors are 4, then zooming in results in 1/4 as many units depicted per pixel. (see

Set Factors...)

Out Multiplies horizontal and vertical scales by the X-factor and Y-factor

(see Set Factors...).

X-Zoom In Divides horizontal scale only, using

X-factor.

X-Zoom Out Multiplies horizontal scale, using

X-factor.



2-10

Option

Y-Zoom In

Y-Zoom Out Multiplies vertical scale only, using

Y-factor.

Square

Divides vertical scale only, using

Y-factor.

Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoom, X-Zoom, or

Y-Zoom.)

Set

Factors...

Sets the X-Zoom and Y-Zoom factors for zooming in or zooming out.

Includes option to recenter the plot before zooming.

Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot, for the supplied x axis settings. (For Sequence and

Statistics aplets, autoscaling rescales both axes.)

The autoscale process uses the first selected function only to determine the best scale to use.

Decimal


Integer

Rescales both axes so each pixel =

0.1 units. Resets default values for

XRNG

(–6.5 to 6.5) and YRNG (–3.1 to

3.2). (Not in Sequence or Statistics aplets.)

Rescales horizontal axis only, making each pixel =1 unit. (Not available in Sequence or Statistics aplets.)

Trig Rescales horizontal axis so

1 pixel = π/24 radians, 7.58, or

8

1

/

3 grads; rescales vertical axis so

1 pixel = 0.1 unit.

(Not in Sequence or Statistics aplets.)



ZOOM examples

Option

Un-zoom


Returns the display to the previous zoom, or if there has been only one zoom, un-zoom displays the graph with the original plot settings.

The following screens show the effects of zooming options on a plot of 3 sin x .

Plot of 3 sin x


Zoom In:

In

Un-zoom:

Un-zoom

Note: Press to move to the bottom of the Zoom list.

Zoom Out:

Out

Now un-zoom.

X-Zoom In:

X-Zoom In

Now un-zoom.

X-Zoom Out:

X-Zoom Out

Now un-zoom.

2-11


Y-Zoom In:

Y-Zoom In

Now un-zoom.

Y-Zoom Out:

Y-Zoom Out

Zoom Square:

Square

To box zoom

The Box Zoom option lets you draw a box around the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle.

1. If necessary, press labels.

to turn on the menu-key

2. Press and select Box...

3. Position the cursor on one corner of the rectangle.

Press .

4. Use the cursor keys

( , etc.) to drag to the opposite corner.

5. Press to zoom in on the boxed area.



To set zoom factors

1. In the Plot view, press .

2. Press .

3. Select Set Factors... and press .

4. Enter the zoom factors. There is one zoom factor for the horizontal scale ( XZOOM) and one for the vertical scale ( YZOOM).

Zooming out multiplies the scale by the factor, so that a greater scale distance appears on the screen.

Zooming in divides the scale by the factor, so that a shorter scale distance appears on the screen.

Other views for scaling and splitting the graph

The preset viewing options menu ( ) contains options for drawing the plot using certain pre-defined configurations. This is a shortcut for changing Plot view settings. For instance, if you have defined a trigonometric function, then you could select Trig to plot your function on a trigonometric scale. It also contains split-screen options.

In certain aplets, for example those that you download from the world wide web, the preset viewing options menu can also contain options that relate to the aplet.

VIEWS menu options

Press , select an option, and press .

Option

Plot-

Detail

Meaning

Splits the screen into the plot and a close-up.

Plot-Table Splits the screen into the plot and the data table.

Overlay

Plot

Plots the current expression(s)

without erasing any pre-existing plot(s).



Split the screen

2-14

Option Meaning (Continued)

Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot, for the supplied x axis settings. (For Sequence and

Statistics aplets, autoscaling rescales both axes.)

The autoscale process uses the first selected function only to determine the best scale to use.

Decimal Rescales both axes so each pixel =

0.1 unit. Resets default values for

XRNG

(–6.5 to 6.5) and YRNG (–3.1 to

3.2). (Not in Sequence or Statistics aplets.)

Integer

Trig

Rescales horizontal axis only, making each pixel=1 unit. (Not available in Sequence or Statistics aplets.)

Rescales horizontal axis so

1 pixel=π/24 radian, 7.58, or

8

1

/

3

grads; rescales vertical axis so

1 pixel = 0.1 unit.

(Not in Sequence or Statistics aplets.)

The Plot-Detail view can give you two simultaneous views of the plot.

1. Press . .

The graph is plotted twice. You can now zoom in on the right side.

2. Press , select the zoom method and press or

. This zooms the right side. Here is an example of split screen with Zoom In.

– The Plot menu keys are available as for the full plot (for tracing, coordinate display, equation display, and so on).



Overlay plots

Decimal scaling

Integer scaling

Trigonometric scaling


– moves the leftmost cursor to the screen’s left edge and moves the rightmost cursor to the screen’s right edge.

– The plot.

menu key copies the right plot to the left

3. To un-split the screen, press over the whole screen.

. The left side takes

The Plot-Table view gives you two simultaneous views of the plot.

Plot-Table and press . The screen displays the plot on the left side and a table of numbers on the right side.

2. To move up and down the table, use the and cursor keys. These keys move the tra.ce point left or right along the plot, and in the table, the corresponding values are highlighted.

3. To move between functions, use the and cursor keys to move the cursor from one graph to another.

4. To return to a full Numeric (or Plot) view, press

(or ).

If you want to plot over an existing plot without erasing that plot, then use Overlay Plot instead of

. Note that tracing follows only the current functions from the current aplet.

Decimal scaling is the default scaling. If you have changed the scaling to Trig or Integer, you can change it back with Decimal.

Integer scaling compresses the axes so that each pixel is

1 1 and the origin is near the screen center.

Use trigonometric scaling whenever you are plotting an expression that includes trigonometric functions.

Trigonometric plots are more likely to intersect the axis at points factored by π.

2-15


About the numeric view

After entering and selecting

(check marking) the expression or expressions that you want to explore in the Symbolic view, press

to view a table of data values for the independent variable (X, T, θ, or N) and dependent variables.

Setting up the table (Numeric view setup)

Press NUM to define any of the table settings.

Use the Numeric Setup input form to configure the table.

1. Highlight the field to edit. Use the arrow keys to move from field to field.

– If there is a number to enter, type it in and press

or . To modify an existing number, press .

– If there is an option to choose, press highlight your choice, and press

,

or .

– Shortcut: Press the key to copy values from the Plot Setup into NUMSTART and

NUMSTEP. Effectively, the menu key allows you to make the table match the pixel columns in the graph view.

2. When done, press numbers.

to view the table of



Numeric view settings

The following table details the fields on the Numeric

Setup input form.

Field

NUMSTART

NUMSTEP

NUMTYPE

NUMZOOM

Meaning

The independent variable’s starting value.

The size of the increment from one independent variable value to the next.

Type of numeric table: Automatic or Build Your Own. To build your own table, you must type each independent value into the table yourself.

Allows you to zoom in or out on a selected value of the independent variable.

Reset numeric settings

To reset the default values for all table settings, press

CLEAR .

Exploring the table of numbers

NUM view menu keys

The following table details the menu keys that you use to work with the table of numbers.

Key Meaning

Displays ZOOM menu list.

Toggles between two character sizes.

Displays the defining function expression for the highlighted column. To cancel this display, press

.

Zoom within a table


Zooming redraws the table of numbers in greater or lesser detail.

2-17


ZOOM options

The following table lists the zoom options:

Option

In

Out

Decimal

Integer

Trig

Un-zoom

Meaning

Decreases the intervals for the independent variable so a narrower range is shown. Uses the NUMZOOM factor in Numeric Setup.

Increases the intervals for the independent variable so that a wider range is shown. Uses the

NUMZOOM factor in Numeric Setup.

Changes intervals for the independent variable to 0.1 units.

Starts at zero. (Shortcut to changing

NUMSTART and NUMSTEP.)

Changes intervals for the independent variable to 1 unit.

Starts at zero. (Shortcut to changing

NUMSTEP.)

Changes intervals for independent variable to π/24 radian or 7.5 degrees or 8

1

/

3

grads. Starts at zero.

Returns the display to the previous zoom.

The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4.

Automatic recalculation

H I N T To jump to an independent variable value in the table, use the arrow keys to place the cursor in the independent variable column, then enter the value to jump to.

You can enter any new value in the X column. When you press , the values for the dependent variables are recalculated, and the entire table is regenerated with the same interval between X values.



Building your own table of numbers

The default NUMTYPE is “Automatic”, which fills the table with data for regular intervals of the independent (X, T, θ, or N) variable. With the NUMTYPE option set to “Build

Your Own”, you fill the table yourself by typing in the independent-variable values you want. The dependent values are then calculated and displayed.

Build a table

1. Start with an expression defined (in Symbolic view) in the aplet of your choice. Note: Function, Polar,

Parametric, and Sequence aplets only.

2. In the Numeric Setup ( NUM

NUMTYPE: Build Your Own.

), choose

3. Open the Numeric view ( ).

4. Clear existing data in the table ( CLEAR ).

5. Enter the independent values in the left-hand column.

Type in a number and press . You do not have to enter them in order, because the function can rearrange them. To insert a number between two others, use .

You enter numbers into the X column

F1 and F2 entries are generated automatically

Clear data

Press CLEAR , to erase the data from a table.



“Build Your Own” menu keys

Key

CLEAR

Meaning

Puts the highlighted independent value (X, T, θ, or N) into the edit line. Pressing replaces this variable with its current value.

Inserts a zero value at the position of the highlight. Replace a zero by typing the number you want and pressing .

Sorts the independent variable values into ascending or descending order. Press and select the ascending or descending option from the menu, and press .

Toggles between two character sizes.

Displays the defining function expression for the highlighted column.

Deletes the highlighted row.

Clears all data from the table.

Example: plotting a circle

Plot the circle, x

2

+ y

2

= 9. First rearrange it to read y = ± –

2

.

To plot both the positive and negative y values, you need to define two equations as follows: y = –

2

and y = –

2



1. In the Function aplet, specify the functions.

Select

Function

9

9

2. Reset the graph setup to the default settings.

SETUP

-

PLOT

CLEAR

3. Plot the two functions and hide the menu so that you can see all the circle.

4. Reset the numeric setup to the default settings.

SETUP NUM

CLEAR

5. Display the functions in numeric form.




3

Function aplet

About the Function aplet

The Function aplet enables you to explore up to 10 real-valued, rectangular functions y in terms of x. For

Once you have defined a function you can:

• create graphs to find roots, intercepts, slope, signed area, and extrema

• create tables to evaluate functions at particular values.

This chapter demonstrates the basic tools of the Function

aplet by stepping you through an example. See “Aplet views” on page 2-1 for further information about the

functionality of the Symbolic, Numeric, and Plot views.

Getting started with the Function aplet

The following example involves two functions: a linear function y = ( y 1 x

)

=

2

– 2 .

and a quadratic equation

Open the

Function aplet

1. Open the Function aplet.

Select Function

The Function aplet starts in the Symbolic view.

The Symbolic view is the defining view for Function,

Parametric, Polar, and Sequence aplets. The other views are derived from the symbolic expression.

Function aplet 3-1


Define the expressions

Set up the plot

2. There are 10 function definition fields on the Function aplet’s Symbolic view screen. They are labeled F1(X) to F0(X). Highlight the function definition field you want to use, and enter an expression. (You can press

to delete an existing line, or clear all lines.)

CLEAR to

1

2

3

You can change the scales of the x and y axes, graph resolution, and the spacing of the axis ticks.

3. Display plot settings.

SETUP

-

PLOT

Plot the functions

Note: For our example, you can leave the plot settings at their default values since we will be using the Auto Scale feature to choose an appropriate y axis for our x axis settings. If your settings do not match this example, press default values.

CLEAR to restore the

4. Specify a grid for the graph.

5. Plot the functions.

3-2 Function aplet


Change the scale

6. You can change the scale to see more or less of your graphs. In this example, choose Auto Scale. (See

“VIEWS menu options” on page 2-13 for a

description of Auto Scale).

Select Auto

Scale

Trace a graph

7. Trace the linear function.

6 times

Note: By default, the

tracer is active.

8. Jump from the linear function to the quadratic function.

Function aplet 3-3


Analyse graph with FCN functions

9. Display the Plot view menu.

To find a root of the quadratic function

From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet

(and any Function-based aplets). The FCN functions

act on the currently selected graph. See “FCN functions” on page 3-10 for further information.

10.Move the cursor to the graph of the quadratic equation by pressing the or key. Then move the cursor so that it is near x = – 1 by pressing the

or key.

Select Root

To find the intersection of the two functions

The root value is displayed at the bottom of the screen.

Note: If there is more than one root (as in our example), the coordinates of the root closest to the current cursor

position are displayed.

11.Find the intersection of the two functions.

3-4 Function aplet


12.Choose the linear function whose intersection with the quadratic function you wish to find.

To find the slope of the quadratic function

To find the signed area of the two functions

The coordinates of the intersection point are displayed at the bottom of the screen.

Note: If there is more than one intersection

(as in our example), the coordinates of the intersection point closest to the current cursor position

are displayed.

13.Find the slope of the quadratic function at the intersection point.

Select Slope

The slope value is displayed at the bottom of the screen.

14.To find the area between the two functions in the range –2 ≤ x ≤ –1, first move the cursor to

F1 x = – and select the signed area option.

Select Signed area

Function aplet 3-5


15.Move the cursor to x = –2 by pressing the or key.

16.Press to accept using F2(x) = (x + 3)

2 other boundary for the integral.

– 2 as the

17. Choose the end value for x.

1

The cursor jumps to x = – 1 on the linear function.

To find the extremum of the quadratic

18.Display the numerical value of the integral.

Note: See “Shading area” on page 3-11

for another method of calculating area.

19. Move the cursor to the quadratic equation and find the extremum of the quadratic.

Select Extremum

The coordinates of the extremum are displayed at the bottom of the screen.

3-6 Function aplet


H I N T The Root and Extremum functions return one value only even if the function has more than one root or extremum.

The function finds the value closest to the position of the cursor. You need to re-locate the cursor to find other roots or extrema that may exist.

Display the numeric view

20.Display the numeric view.

Set up the table

21.Display the numeric setup.

SETUP NUM

See “Setting up the table (Numeric view setup)” on page 2-16 for more information.

22. Match the table settings to the pixel columns in the graph view.

Explore the table

23. Display the table of values.

Function aplet 3-7


To navigate around a table

24.Move to X = –5.9.

6 times

To go directly to a value

25. Move directly to X = 10.

1 0

To access the zoom options

26. Zoom in on X = 10 by a factor of 4. Note: NUMZOOM

has a setting of 4.

In

To change font size

27. Display table numbers in large font.

To display the symbolic definition of a column

28.Display the symbolic definition for the F1 column.

The symbolic definition of

F1 is displayed at the bottom of the screen.

3-8 Function aplet


Function aplet interactive analysis

From the Plot view ( ), you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any

Function-based aplets). See “FCN functions” on page 3-

10. The FCN operations act on the currently selected

graph.

The results of the FCN functions are saved in the following variables:

• Area

• Extremum

• Isect

• Root

• Slope

For example, if you use the Root function to find the root of a plot, you can use the result in calculations in HOME.

Access FCN variables

Function aplet

The FCN variables are contained on the VARS menu.

To access FCN variables in HOME:

Select Plot FCN or to choose a variable

To access FCN variable in the Function aplet’s Symbolic view:

Select Plot FCN or to choose a variable

3-9


FCN functions

The FCN functions are:

Function

Root

Extremum

Slope

Signed area

Description

Select Root to find the root of the current function nearest the cursor. If no root is found, but only an extremum, then the result is labeled EXTR: instead of ROOT:.

(The root-finder is also used in the

Solve aplet. See also “Interpreting results” on page 7-6.) The cursor

is moved to the root value on the x-axis and the resulting x-value is saved in a variable named

ROOT.

Select Extremum to find the maximum or minimum of the current function nearest the cursor. This displays the coordinate values and moves the cursor to the extremum. The resulting value is saved in a variable named EXTREMUM.

Select Slope to find the numeric derivative at the current position of the cursor. The result is saved in a variable named SLOPE.

Select Signed area to find the numeric integral. (If there are two or more expressions checkmarked, then you will be asked to choose the second expression from a list that includes the x-axis.) Select a starting point, then move the cursor to selection ending point.

The result is saved in a variable named AREA.

3-10 Function aplet


Function Description (Continued)

Intersection Select Intersection to find the intersection of two graphs nearest the cursor. (You need to have at least two selected expressions in

Symbolic view.) Displays the coordinate values and moves the cursor to the intersection. (Uses

Solve function.) The resulting xvalue is saved in a variable named ISECT.

Shading area

You can shade a selected area between functions. This process also gives you an approximate measurement of the area shaded.

1. Open the Function aplet. The Function aplet opens in the Symbolic view.

2. Select the expressions whose curves you want to study.

3. Press to plot the functions.

4. Press or to position the cursor at the starting point of the area you want to shade.

5. Press .

6. Press , Signed area and press

.

7. Press , choose the function that will act as the boundary of the shaded area, and press .

8. Press the or key to shade in the area.

9. Press to calculate the area. The area measurement is displayed near the bottom of the screen.

To remove the shading, press to re-draw the plot.

Function aplet 3-11


Plotting a piecewise-defined function

Suppose you wanted to plot the following piecewisedefined function.

=

⎧

⎪

⎨

⎪

⎩

+ ; x ≤ – 1 x

2

; – 1 < ≤

– ; x 1

1. Open the Function aplet.

Select

Function

2. Highlight the line you want to use, and enter the expression. (You can press to delete an existing line, or CLEAR to clear all lines.)

2

CHARS

≤

1

CHARS > 1

AND CHARS

≤ 1

4

CHARS

> 1

Note: You can use the menu key to assist in the

entry of equations. It has the same effect as pressing

.

3-12 Function aplet


4

Parametric aplet

About the Parametric aplet

The Parametric aplet allows you to explore parametric equations. These are equations in which both x and y are defined as functions of t. They take the forms

= ( ) x = f t

Getting started with the Parametric aplet

The following example uses the parametric equations x t y t

=

= 3

3 sin cos t t

Note: This example will produce a circle. For this example to work, the angle measure must be set to degrees.

Open the

Parametric aplet

1. Open the Parametric aplet.

Select

Parametric

Define the expressions

2. Define the expressions.

3

3

Parametric aplet 4-1


Set angle measure

3. Set the angle measure to degrees.

MODES

Select Degrees

Set up the plot

4. Display the graphing options.

PLOT

The Plot Setup input form has two fields not included in the Function aplet, TRNG and TSTEP. TRNG specifies the range of t values. TSTEP specifies the step value between t values.

5. Set the TRNG and TSTEP so that t steps from 0° to

360° in 5° steps.

360

5

Plot the expression

6. Plot the expression.

7. To see all the circle, press twice.

4-2 Parametric aplet


Overlay plot

Display the numbers

8. Plot a triangle graph over the existing circle graph.

PLOT

120

Select Overlay Plot

A triangle is displayed rather than a circle (without changing the equation) because the changed value of TSTEP ensures that points being plotted are 120° apart instead of nearly continuous.

You are able to explore the graph using trace, zoom, split screen, and scaling functionality available in the

Function aplet. See “Exploring the graph” on page 2-

7 for further information.

9. Display the table of values.

You can highlight a

t-value, type in a replacement value, and see the table jump to that value. You can also zoom in or zoom out on any t-value in the table.

You are able to explore the table using ,

, build your own table, and split screen functionality available in the Function aplet. See

“Exploring the table of numbers” on page 2-17 for


Parametric aplet 4-3



5

Polar aplet

Getting started with the Polar aplet

Open the Polar aplet

1. Open the Polar aplet.

Select Polar

Like the Function aplet, the Polar aplet opens in the Symbolic view.

Define the expression

2. Define the polar equation r = 2 π cos (

2 π

2

) cos ( )

2

.

Specify plot settings

3. Specify the plot settings. In this example, we will use the default settings, except for the θ RNG fields.

SETUP PLOT

4

CLEAR

π

Plot the expression

4. Plot the expression.

Polar aplet 5-1


Explore the graph

Display the numbers

5. Display the Plot view menu key labels.

The Plot view options available are the same as those found in the

Function aplet. See

“Exploring the graph” on page 2-7 for further information.

6. Display the table of values for θ and R1.

The Numeric view options available are the same as those found in the Function

aplet. See “Exploring the table of numbers” on page 2-17 for further information.

5-2 Polar aplet


6

Sequence aplet

About the Sequence aplet

The Sequence aplet allows you to explore sequences.

You can define a sequence named, for example, U1:

• in terms of n

• in terms of U1(n–1)

• in terms of U1(n–2)

• in terms of another sequence, for example, U2(n)

• in any combination of the above.

The Sequence aplet allows you to create two types of graphs:

– A Stairsteps graph plots n on the horizontal axis and U n

on the vertical axis.

– A Cobweb graph plots U

n–1 axis and U n

on the horizontal

on the vertical axis.

Getting started with the Sequence aplet

The following example defines and then plots an expression in the Sequence aplet. The sequence illustrated is the well-known Fibonacci sequence where each term, from the third term on, is the sum of the preceding two terms. In this example, we specify three sequence fields: the first term, the second term and a rule for generating all subsequent terms.

However, you can also define a sequence by specifying just the first term and the rule for generating all subsequent terms. You will, though, have to enter the second term if the hp39gs is unable to calculate it automatically. Typically if the nth term in the sequence depends on n–2, then you must enter the second term.

Sequence aplet 6-1


Open the

Sequence aplet

Define the expression

1. Open the Sequence aplet.

Select

Sequence

The Sequence aplet starts in the Symbolic view.

2. Define the Fibonacci sequence, in which each term

(after the first two) is the sum of the preceding two terms:

U

1

= 1 = 1 U n

= U + U

In the Symbolic view of the Sequence aplet, highlight the U 1 (1) field and begin defining your sequence.

1 1

Note: You can use the

, , ,

, and menu keys to assist in the entry of

equations.

Specify plot settings

3. In Plot Setup, first set the SEQPLOT option to

Stairstep. Reset the default plot settings by clearing the Plot Setup view.

SETUP

-

PLOT

CLEAR

8

8

6-2 Sequence aplet


Plot the sequence

4. Plot the Fibonacci sequence.

5. In Plot Setup, set the SEQPLOT option to Cobweb.

SETUP PLOT

Select Cobweb

Display the table

6. Display the table of values for this example.

Sequence aplet 6-3



7

Solve aplet

About the Solve aplet

The Solve aplet solves an equation or an expression for its unknown variable. You define an equation or expression in the symbolic view, then supply values for all the variables except one in the numeric view. Solve works only with real numbers.

Note the differences between an equation and an expression:

• An equation contains an equals sign. Its solution is a value for the unknown variable that makes both sides have the same value.

• An expression does not contain an equals sign. Its solution is a root, a value for the unknown variable that makes the expression have a value of zero.

You can use the Solve aplet to solve an equation for any one of its variables.

When the Solve aplet is started, it opens in the Solve

Symbolic view.

• In Symbolic view, you specify the expression or equation to solve. You can define up to ten equations

(or expressions), named E0 to E9. Each equation can contain up to 27 real variables, named A to Z and θ.

• In Numeric view, you specify the values of the known variables, highlight the variable that you want to solve for, and press .

You can solve the equation as many times as you want, using new values for the knowns and highlighting a different unknown.

Note: It is not possible to solve for more than one variable at once. Simultaneous linear equations, for example, should be solved using the Linear Solver aplet, matrices or graphs in the Function aplet.

Solve aplet 7-1


Getting started with the Solve aplet

Suppose you want to find the acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distance of 100 m.

The equation to solve is:

V

2

= U

2

+ 2AD

Open the Solve aplet

1. Open the Solve aplet.

Select Solve

Define the equation

Enter known variables

The Solve aplet starts in the symbolic view.

2. Define the equation.

V

U

2

A

D

Note: You can use the menu key to assist in the entry of equations.

3. Display the Solve numeric view screen.

7-2 Solve aplet


Solve the unknown variable

H I N T

4. Enter the values for the known variables.

2 7 7 8

1 6 6 7

1 0 0

(

If the Decimal Mark setting in the Modes input form

MODES ) is set to Comma, use instead of .

5. Solve for the unknown variable (A).

Plot the equation

Therefore, the acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec

(100 kph) in a distance of 100 m is approximately

2.47 m/s

2

.

Because the variable A in the equation is linear we know that we need not look for any other solutions.

The Plot view shows one graph for each side of the selected equation. You can choose any of the variables to be the independent variable.

The current equation is V

2

= U

2

+ 2AD .

One of these is Y = V

2

, with V = 27.78

, that is,

Y = 771.7284

. This graph will be a horizontal line.

The other graph will be Y = U

2

+ 2AD , with

U = 16.67

and D = 100

Y = 200A 277.8889

, that is,

. This graph is also a line. The desired solution is the value of A where these two lines intersect.

Solve aplet 7-3


6. Plot the equation for variable A.

Scale

Select Auto

7. Trace along the graph representing the left side of the equation until the cursor nears the intersection.

20 times

Note the value of A displayed near the bottom left corner of the screen.

The Plot view provides a convenient way to find an approximation to a solution instead of using the

Numeric view Solve option. See “Plotting to find guesses” on page 7-7 for more information.

Solve aplet’s NUM view keys

The Solve aplet’s NUM view keys are:

Key Meaning

Copies the highlighted value to the edit line for editing. Press when done.

Displays a message about the

solution (see “Interpreting results” on page 7-6).

Displays other pages of variables, if any.

Displays the symbolic definition of the current expression. Press when done.

Finds a solution for the highlighted variable, based on the values of the other variables.

7-4 Solve aplet


Key

CLEAR


Clears highlighted variable to zero or deletes current character in edit line, if edit line is active.

Resets all variable values to zero or clears the edit line, if cursor is in edit line.

Use an initial guess

You can usually obtain a faster and more accurate solution if you supply an estimated value for the unknown variable before pressing . Solve starts looking for a solution at the initial guess.

Before plotting, make sure the unknown variable is highlighted in the numeric view. Plot the equation to help you select an initial guess when you don’t know the range

in which to look for the solution. See “Plotting to find guesses” on page 7-7 for further information.

H I N T An initial guess is especially important in the case of a curve that could have more than one solution. In this case, only the solution closest to the initial guess is returned.

Number format

You can change the number format for the Solve aplet in the Numeric Setup view. The options are the same as in

HOME MODES: Standard, Fixed, Scientific, and

Engineering. For the latter three, you also specify how

many digits of accuracy you want. See “Mode settings” on page 1-10 for more information.

You might find it handy to set a different number format for the Solve aplet if, for example, you define equations to solve for the value of money. A number format of

Fixed 2 would be appropriate in this case.

Solve aplet 7-5


Interpreting results

After Solve has returned a solution, press in the

Numeric view for more information. You will see one of the following three messages. Press to clear the message.

Message

Zero

Sign Reversal

Extremum

Condition

The Solve aplet found a point where both sides of the equation were equal, or where the expression was zero (a root), within the calculator's

12-digit accuracy.

Solve found two points where the difference between the two sides of the equation has opposite signs, but it cannot find a point in between where the value is zero. Similarly, for an expression, where the value of the expression has different signs but is not precisely zero. This might be because either the two points are neighbours (they differ by one in the twelfth digit), or the equation is not real-valued between the two points.

Solve returns the point where the value or difference is closer to zero.

If the equation or expression is continuously real, this point is

Solve’s best approximation of an actual solution.

Solve found a point where the value of the expression approximates a local minimum (for positive values) or maximum (for negative values).

This point may or may not be a solution.

Or: Solve stopped searching at

9.99999999999E499, the largest number the calculator can represent.

Note that the value returned is probably not valid.

7-6 Solve aplet


If Solve could not find a solution, you will see one of the following two messages.

Message

Bad Guess(es)

Constant?

Condition

The initial guess lies outside the domain of the equation.

Therefore, the solution was not a real number or it caused an error.

The value of the equation is the same at every point sampled.

H I N T It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero. Only by checking the information will you know that this is the case.

The Root-Finder at work

You can watch the process of the root-finder calculating and searching for a root. Immediately after pressing

to start the root-finder, press any key except .

You will see two intermediate guesses and, to the left, the sign of the expression evaluated at each guess. For example:

+ 2 2.219330555745

– 1 21.31111111149

You can watch as the root-finder either finds a sign reversal or converges on a local extrema or does not converge at all. If there is no convergence in process, you might want to cancel the operation (press ) and start over with a different initial guess.

Plotting to find guesses

The main reason for plotting in the Solve aplet is to help you find initial guesses and solutions for those equations that have difficult-to-find or multiple solutions.

Consider the equation of motion for an accelerating body:

X = V

0

T +

AT

2

2

Solve aplet 7-7


7-8 where X is distance, V

0

is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and

Y = V

0

T + (AT

2

) / 2.

Since this equation is quadratic for T, there can be both a positive and a negative solution. However, we are concerned only with positive solutions, since only positive distance makes sense.

1. Select the Solve aplet and enter the equation.

Select Solve

X

V

T

A

T 2

2. Find the solution for T (time) when X=30, V=2, and

A=4. Enter the values for X, V, and A; then highlight the independent variable, T.

30

2

4

to highlight T

3. Use the Plot view to find an initial guess for T. First set appropriate X and Y ranges in the Plot Setup. With equation X = V x T + A x T

2

/2, the plot will produce two graphs: one for

X = V x T + A x T

2

Y = X and one for

/2. Since we have set this example, one of the graphs will be Y

X

=

= 30

30 .

in

Therefore, make the YRNG –5 to 35. Keep the XRNG default of – 6.5 to 6.5.

SETUP PLOT

5 35

4. Plot the graph.

Solve aplet


5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T.

Press until the cursor is at the intersection.

The two points of intersection show that there are two solutions for this equation. However, only positive values for X make sense, so we want to find the solution for the intersection on the right side of the y-axis.

6. Return to the Numeric view.

Note: the T-value is filled in with the position of the cursor from the Plot view.

7. Ensure that the T value is highlighted, and solve the equation.

Use this equation to solve for another variable, such as velocity. How fast must a body’s initial velocity be in order for it to travel 50 m within 3 seconds? Assume the same acceleration, 4 m/s

2

. Leave the last value of V as the initial guess.

3

50

Solve aplet 7-9


Using variables in equations

You can use any of the real variable names, A to Z and

θ. Do not use variable names defined for other types, such as M1 (a matrix variable).

Home variables

All home variables (other than those for aplet settings, like

Xmin and Ytick) are global, which means they are

shared throughout the different aplets of the calculator. A value that is assigned to a home variable anywhere remains with that variable wherever its name is used.

H I N T

Therefore, if you have defined a value for T (as in the above example) in another aplet or even another Solve equation, that value shows up in the Numeric view for this

Solve equation. When you then redefine the value for T in this Solve equation, that value is applied to T in all other contexts (until it is changed again).

This sharing allows you to work on the same problem in different places (such as HOME and the Solve aplet) without having to update the value whenever it is recalculated.

As the Solve aplet uses existing variable values, be sure to check for existing variable values that may affect the solve process. (You can use CLEAR to reset all values to zero in the Solve aplet’s Numeric view if you wish.)

Aplet variables

Functions defined in other aplets can also be referenced in the Solve aplet. For example, if, in the Function aplet, you define F1(X)=X

2

+10, you can enter F1(X)=50 in the Solve aplet to solve the equation X

2

+10=50.

7-10 Solve aplet


8

Linear Solver aplet

About the Linear Solver aplet

The Linear Solver aplet allows you to solve a set of Linear

Equations. The set can contain two or three linear equations.

In a two-equation set, each equation must be in the form

= k . In a three-equation set, each equation must be in the form + + = k .

You provide values for a, b, and k (and c in threeequation sets) for each equation, and the Linear Solver aplet will attempt to solve for x and y (and z in threeequation sets).

The hp39gs will alert you if no solution can be found, or if there is an infinite number of solutions.

Note that the Linear Solver aplet only has a numeric view.

Getting started with the Linear Solver aplet

The following example defines a set of three equations and then solves for the unknown variables.

Open the

Linear Solver aplet

1. Open the Linear Sequence aplet.

Select Linear

Solver

The Linear Equation

Solver opens.

Linear Solver aplet 8-1


Choose the equation set

Define and solve the equations

8-2

2. If the last time you used the Linear Solver aplet you solved for two equations, the twoequation input form is displayed (as in the example in the previous step). To solve a three-equation set, press

. Now the input form displays three equations.

If the three-equation input form is displayed and you want to solve a two-equation set, press .

In this example, we are going to solve the following equation set:

= 5

= 10

= 6

Hence we need the three-equation input form.

3. You define the equations you want to solve by entering the co-efficients of each variable in each equation and the constant term. Notice that the cursor is immediately positioned at the co-efficient of x in the first equation. Enter that co-efficient and press or

.

4. The cursor moves to the next co-efficient. Enter that coefficient, press or , and continue doing likewise until you have defined all the equations.

Note: you can enter the name of a variable for any co-efficient or constant. Press entering the name. The

and begin

menu key appears.

Press that key to lock alphabetic entry mode. Press it again to cancel the lock.

Once you have entered enough values for the solver to be able to generate solutions, those solutions appear on the display. In the example at the right, the solver was able to find solutions for x, y, and z as

Linear Solver aplet

HP 39gs English.book Page 3 Wednesday, December 7, 2005 11:24 PM soon as the first co-efficient of the last equation was entered.

As you enter each of the remaining known values, the solution changes. The example at the right shows the final solution once all the co-efficients and constants are entered for the set of equations we set out to solve.

Linear Solver aplet 8-3



9

Triangle Solve aplet

About the Triangle Solver aplet

The Triangle Solver aplet allows you to determine the length of a side of a triangle, or the angle at the vertex of a triangle, from information you supply about the other lengths and/or other angles.

You need to specify at least three of the six possible values—the lengths of the three sides and the size of the three angles—before the solver can calculate the other values. Moreover, at least one value you specify must be a length. For example, you could specify the lengths of two sides and one of the angles; or you could specify two angles and one length; or all three lengths. In each case, the solver will calculate the remaining lengths or angles.

The hp39gs will alert you if no solution can be found, or if you have provided insufficient data.

If you are determining the properties of a right-angled triangle, a simpler input form is available by pressing the menu key.

Note that the Triangle Solver aplet only has a numeric view.

Getting started with the Triangle Solver aplet

The following example solves for the unknown length of the side of a triangle whose two known sides—of lengths

4 and 6—meet at an angle of 30 degrees.

Before you begin: You should make sure that your angle measure mode is appropriate. If the angle information you have is in degrees (as in this example) and your current angle measure mode is radians or grads, change the mode to degrees before running the solver. (See

“Mode settings” on page 1-10 for instructions.) Because

the angle measure mode is associated with the aplet, you should start the aplet first and then change the setting.

Triangle Solve aplet 9-1


Open the

Triangle

Solver aplet

Choose the triangle type

Specify the known values

9-2

1. Open the Triangle Solver aplet.

Select

Triangle Solver

The Triangle Solver aplet opens.

Note: if you have already used the Triangle Solver, the entries and results from the previous use will still be displayed. To start the Triangle Solver afresh, clear the previous entries and results by pressing

CLEAR.

2. If the last time you used the Triangle Solver aplet you used the right-angled triangle input form, that input form is displayed again (as in the example at the right). If the triangle you are investigating is not a right-angled triangle, or you are not sure what type it is, you should use the general input form (illustrated in the previous step). To switch to the general input form, press .

If the general input form is displayed and you are investigating a right-angled triangle, press display the simpler input form.

to

3. Using the arrow keys, move to a field whose value you know, enter the value and press or

Repeat for each known value.

.

Note that the lengths of the sides are labeled

A, B, and C, and the angles are labeled

α

,

β , and δ . It is important that you enter the known values in the appropriate fields. In our example, we know the length of two sides and the angle at which those sides meet. Hence if we specify the lengths of sides A and B, we must enter the angle as δ (since δ is the angle where A and B meet). If instead we entered the

Triangle Solve aplet


Errors

Triangle Solve aplet lengths as B and C, we would need to specify the angle as α . The illustration on the display will help you determine where to enter the known values.

Note: if you need to change the angle measure mode, press MODES, change the mode, and then press to return to the aplet.

calculates the values of the unknown variables and displays. As the illustration at the right shows, the length of the unknown side in our example is 3.2296. (The other two angles have also been calculated.)

Note: if two sides and an adjacent acute angle are entered and there are two solutions, only one will be displayed initially.

In this case, an menu key is displayed

(as in this example).

You press to display the second solution, and again to return to the first solution.

No solution with given data

If you are using the general input form and you enter more than 3 values, the values might not be consistent, that is, no triangle could possibly have all the values you specified.

In these cases, No sol with given data appears on the screen.

The situation is similar if you are using the simpler input form (for a right-angled triangle) and you enter more than two values.

9-3


Not enough data

If you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the remaining attributes of the triangle. If you specify less than three, Not enough data appears on the screen.

If you are using the simplified input form (for a rightangled triangle), you must specify at least two values.

In addition, you cannot specify only angles and no lengths.

9-4 Triangle Solve aplet


10

Statistics aplet

About the Statistics aplet

The Statistics aplet can store up to ten data sets at one time. It can perform one-variable or two-variable statistical analysis of one or more sets of data.

The Statistics aplet starts with the Numeric view which is used to enter data. The Symbolic view is used to specify which columns contain data and which column contains frequencies.

You can also compute statistics values in HOME and recall the values of specific statistics variables.

The values computed in the Statistics aplet are saved in variables, and many of these variables are listed by the

function accessible from the Statistics aplet’s

Numeric view screen.

Getting started with the Statistics aplet

The following example asks you to enter and analyze the advertising and sales data (in the table below), compute statistics, fit a curve to the data, and predict the effect of more advertising on sales.

Advertising minutes

(independent, x)

2

1

5

4

3

5

Resulting Sales ($)

(dependent, y)

1400

920

1100

2265

2890

2200

Statistics aplet 10-1


Open the


Enter data

1. Open the Statistics aplet and clear existing data by pressing .

Select Statistics

The Statistics aplet starts in the Numerical view.

1VAR/2VAR menu key label

At any time the Statistics aplet is configured for only one of two types of statistical explorations: onevariable ( ) or two-variable ( ). The 5th menu key label in the Numeric view toggles between these two options and shows the current option.

2. Select .

You need to select because in this example we are analyzing a dataset comprising two variables: advertising minutes and resulting sales.

3. Enter the data into the columns.

2 1

3 5

5 4

to move to the next column

10-2 Statistics aplet


Choose fit and data columns

4. Select a fit in the Symbolic setup view.

SETUP SYMB

Select Linear

You can create up to five explorations of two-variable data, named S1 to S5. In this example, we will create just one: S1.

5. Specify the columns that hold the data you want to analyze.

You could have entered your data into columns other than C1 and C2.

Explore statistics

6. Find the mean advertising time ( MEANX) and the mean sales ( MEANY).

MEANX is 3.3 minutes and MEANY is about

$1796.

7. Scroll down to display the value for the correlation coefficient ( CORR). The CORR value indicates how well the linear model fits the data.

9 times

The value is .8995.



Setup plot

Plot the graph

8. Change the plotting range to ensure all the data points are plotted (and select a different point mark, if you wish).

SETUP PLOT

7

100

4000

9. Plot the graph.

Draw the regression curve

10.Draw the regression curve (a curve to fit the data points).

Display the equation for best linear fit

This draws the regression line for the best linear fit.

11.Return to the Symbolic view.

10-4

12.Display the equation for the best linear fit.

to move to the

FIT1 field

The full FIT1 expression is shown.

The slope (m) is 425.875. The y-intercept (b) is

376.25.

Statistics aplet


Predict values

13.To find the predicted sales figure if advertising were to go up to 6 minutes:

S (to highlight

Stat-Two)

(to highlight

PREDY)

6

14.Return to the Plot view.

15.Jump to the indicated point on the regression line.

6

Observe the predicted

y-value in the left bottom corner of the screen.



Entering and editing statistical data

The Numeric view ( ) is used to enter data into the

Statistics aplet. Each column represents a variable named

C0 to C9. After entering the data, you must define the data set in the Symbolic view ( ).

H I N T A data column must have at least four data points to provide valid two-variable statistics, or two data points for one-variable statistics.

You can also store statistical data values by copying lists from HOME into Statistics data columns. For example, in

HOME, L1 C1 stores a copy of the list L1 into the data-column variable C1.

Statistics aplet’s NUM view keys

The Statistics aplet’s Numeric view keys are:

Key Meaning

Copies the highlighted item into the edit line.

Inserts a zero value above the highlighted cell.

Sorts the specified independent data column in ascending or descending order, and rearranges a specified dependent (or frequency) data column accordingly.

Switches between larger and smaller font sizes.

A toggle switch to select onevariable or two-variable statistics.

This setting affects the statistical calculations and plots. The label indicates which setting is current.

Computes descriptive statistics for each data set specified in Symbolic view.



Example

Statistics aplet

Key

CLEAR cursor key


Deletes the currently highlighted value.

Clears the current column or all columns of data. Pregss

CLEAR to display a menu list, then select the current column or all columns option, and press .

Moves to the first or last row, or first or last column.

You are measuring the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 170cm,

175cm, 180cm.

1. Open the Statistics aplet.

Select

Statistics

2. Enter the measurement data.

160

165

170

175

180

3. Find the mean of the sample.

Ensure the /

menu key label reads .

Press

to see the statistics calculated from the sample data in C1.

10-7


10-8

Note that the title of the column of statistics is

H1. There are 5 data set definitions available for one-variable statistics: H1–H5. If data is entered in C1, H1 is automatically set to use

C1 for data, and the frequency of each data point is set to 1. You can select other columns of data from the Statistics Symbolic setup view.

4. Press to close the statistics window and press key to see the data set definitions.

The first column indicates the associated column of data for each data set definition, and the second column indicates the constant frequency, or the column that holds the frequencies.

The keys you can use from this window are:

Key

or

Meaning

Copies the column variable (or variable expression) to the edit line for editing. Press when done.

Checks/unchecks the current data set. Only the checkmarked data set(s) are computed and plotted.

Typing aid for the column variables

( ) or for the Fit expressions ( ).

Displays the current variable expression in standard mathematical form. Press when done.

Evaluates the variables in the highlighted column (C1, etc.) expression.

Statistics aplet


Statistics aplet

Key

CLEAR


Displays the menu for entering variable names or contents of variables.

Displays the menu for entering math operations.

Deletes the highlighted variable or the current character in the edit line.

Resets default specifications for the data sets or clears the edit line (if it was active).

Note: If CLEAR is used the

data sets will need to be selected

again before re-use.

To continue our example, suppose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded. Instead of entering all the new data in C1, we shall simply add another column, C2, that holds the frequencies of our five data points in C1.

Height

(cm)

160

165

170

175

180

5. Move the highlight bar into the right column of the H1 definition and replace the frequency value of 1 with the name C2.

2

Frequency

8

2

5

3

1

10-9


6. Return to the numeric view.

7. Enter the frequency data shown in the above table.

5

2

1

3

8

8. Display the computed statistics.

The mean height is approximately

167.63cm.

9. Setup a histogram plot for the data.

SETUP

-

PLOT

Enter set up information appropriate to your data.

10.Plot a histogram of the data.

Save data

Edit a data set

The data that you enter is automatically saved. When you are finished entering data values, you can press a key for another Statistics view (like another aplet or HOME.

), or you can switch to

In the Numeric view of the Statistics aplet, highlight the data value to change. Type a new value and press , or press line for modification. Press value on the edit line.

to copy the value to the edit

after modifying the



Delete data

Insert data

Sort data values

• To delete a single data item, highlight it and press

. The values below the deleted cell will scroll up one row.

• To delete a column of data, highlight an entry in that column and press name.

CLEAR . Select the column

• To delete all columns of data, press

Select All columns.

CLEAR .

Highlight the entry following the point of insertion. Press

, then enter a number. It will write over the zero that was inserted.

1. In Numeric view, highlight the column you want to sort, and press .

2. Specify the Sort Order. You can choose either

Ascending or Descending.

3. Specify the INDEPENDENT and DEPENDENT data columns. Sorting is by the independent column. For instance, if Age is C1 and Income is C2 and you want to sort by Income, then you make C2 the independent column for the sorting and C1 the dependent column.

– To sort just one column, choose None for the dependent column.

– For one-variable statistics with two data columns, specify the frequency column as the dependent column.

4. Press .



Defining a regression model

The Symbolic view includes an expression (Fit1 through

Fit5) that defines the regression model, or “fit”, to use for the regression analysis of each two-variable data set.

There are three ways to select a regression model:

• Accept the default option to fit the data to a straight line.

• Select one of the available fit options in Symbolic

Setup view.

• Enter your own mathematical expression in Symbolic view. This expression will be plotted, but it will not be

fitted to the data points.

Angle Setting

You can ignore the angle measurement mode unless your

Fit definition (in Symbolic view) involves a trigonometric function. In this case, you should specify in the mode screen whether the trigonometric units are to be interpreted in degrees, radians, or grads.

To choose the fit

1. In Numeric view, make sure is set.

2. Press SETUP

-

SYMB

to display the Symbolic Setup view. Highlight the Fit number ( S1FIT to S5FIT) you want to define.

3. Press and select from the list. Press when done. The regression formula for the fit is displayed in

Symbolic view.

Fit models

Ten fit models are available:

Fit model

Linear

Logarithmic

Exponential

Power

Meaning

(Default.) Fits the data to a straight line, y = mx+b. Uses a least-squares fit.

Fits to a logarithmic curve,

y = m lnx + b.

Fits to an exponential curve, y = be mx

.

Fits to a power curve, y = bx m

.



To define your own fit

Fit model

Quadratic

Cubic

Logistic


Fits to a quadratic curve, y = ax

2

+bx+c. Needs at least three points.

Fits to a cubic curve, y = ax

3

+bx

2

+cx+d. Needs at least four points.

Fits to a logistic curve,

Exponent y =

+

( – bx )

, where L is the saturation value for growth. You can store a positive real value in L, or—if L=0—let L be computed automatically.

Fits to an exponent curve, y = ab x

.

Trigonometric Fits to a trigonometric curve, y = a ⋅ sin ( ) + d . Needs at least three points.

User Defined Define your own expression (in

Symbolic view.)

1. In Numeric view, make sure is set.

2. Display the Symbolic view.

3. Highlight the Fit expression ( Fit1, etc.) for the desired data set.

4. Type in an expression and press .

The independent variable must be X, and the expression must not contain any unknown variables.

Example: 1.5

× cos x + 0.3

× sin x .

This automatically changes the Fit type ( S1FIT, etc.) in the Symbolic Setup view to User Defined.



Computed statistics

One-variable

Statistic

NΣ

TOTΣ

MEANΣ

PVARΣ

SVARΣ

PSDEV

SSDEV

MINΣ

Q1

MEDIAN

Q3

Definition

Number of data points.

Sum of data values (with their frequencies).

Mean value of data set.

Population variance of data set.

Sample variance of data set.

Population standard deviation of data set.

Sample standard deviation of data set.

Minimum data value in data set.

First quartile: median of values to left of median.

Median value of data set.

Third quartile: median of values to right of median.

Maximum data value in data set.

MAXΣ

When the data set contains an odd number of values, the data set’s median value is not used when calculating Q1 and Q3 in the table above. For example, for the following data set:

{ 3,5,7,8,15,16,17} only the first three items, 3, 5, and 7 are used to calculate

Q1, and only the last three terms, 15, 16, and 17 are used to calculate Q3.



Two-variable

Plotting

Statistics aplet

Statistic

MEANX

Σ X

Σ X2

MEANY

Σ Y

Σ Y2

Σ XY

SCOV

PCOV

CORR

RELERR

Definition

Mean of x- (independent) values.

Sum of x-values.

Sum of x

2

-values.

Mean of y- (dependent) values.

Sum of y-values.

Sum of y

2

-values.

Sum of each xy.

Sample covariance of independent and dependent data columns.

Population covariance of independent and dependent data columns

Correlation coefficient of the independent and dependent data columns for a linear fit only

(regardless of the Fit chosen).

Returns a value from 0 to 1, where

1 is the best fit.

The relative error for the selected fit. Provides a measure of accuracy for the fit.

You can plot:

• histograms ( )

• box-and-whisker plots ( )

• scatter plots ( ).

Once you have entered your data ( data set (

), defined your

), and defined your Fit model for twovariable statistics ( SETUP SYMB ), you can plot your data. You can plot up to five scatter or box-and-whisker plots at a time. You can plot only one histogram at a time.

10-15


To plot statistical data

1. In Symbolic view ( sets you want to plot.

), select ( ) the data

2. For one-variable data (

Plot Setup ( SETUP

), select the plot type in

PLOT ). Highlight STATPLOT, press , select either Histogram or

BoxWhisker, and press .

3. For any plot, but especially for a histogram, adjust the plotting scale and range in the Plot Setup view. If you find histogram bars too fat or too thin, you can adjust them by adjusting the HWIDTH setting.

4. Press . If you have not adjusted the Plot Setup yourself, you can try select Auto Scale

.

Auto Scale can be relied upon to give a good starting scale which can then be adjusted in the Plot Setup view.

Plot types

Histogram

Box and

Whisker Plot

One-variable statistics.

The numbers below the plot mean that the current bar

(where the cursor is) starts at

0 and ends at 2 (not including 2), and the frequency for this column, (that is, the number of data elements that fall between 0 and 2) is 1. You can see information about the next bar by pressing the key.

One-variable statistics.

The left whisker marks the minimum data value. The box marks the first quartile, the median (where the cursor is), and the third quartile.

The right whisker marks the maximum data value. The numbers below the plot mean that this column has a median of 13.



Scatter Plot

Two-variable statistics.

The numbers below the plot indicate that the cursor is at the first data point for S2, at

(1, 6). Press to move to the next data point and display information about it.

To connect the data points as they are plotted, checkmark

CONNECT in the second page of the Plot Setup. This is not a regression curve.

Fitting a curve to 2VAR data

In the Plot view, press . This draws a curve to fit the

checked two-variable data set(s). See “To choose the fit” on page 10-12.

Correlation coefficient

Statistics aplet

The expression in Fit2 shows that the slope=1.98082191781 and the yintercept=2.2657.

The correlation coefficient is stored in the CORR variable.

It is a measure of fit to a linear curve only. Regardless of the Fit model you have chosen, CORR relates to the linear model.

10-17


Relative Error

H I N T

The relative error is a measure of the error between predicted values and actual values based on the specified

Fit. A smaller number means a better fit.

The relative error is stored in a variable named RELERR.

The relative error provides a measure of fit accuracy for all fits, and it does depend on the Fit model you have chosen.

In order to access the CORR and RELERR variables after you plot a set of statistics, you must press the numeric view and then

to access

to display the correlation values. The values are stored in the variables when you access the Symbolic view.

Setting up the plot (Plot setup view)

The Plot Setup view ( SETUP PLOT ) sets most of the same plotting parameters as it does for the other built-in aplets.

See “About the Plot view” on page 2-5. Settings unique

to the Statistics aplet are as follows:

Plot type (1VAR)

STATPLOT enables you to specify either a histogram or a box-and-whisker plot for one-variable statistics (when

is set). Press to change the highlighted setting

Histogram width

HWIDTH enables you to specify the width of a histogram bar. This determines how many bars will fit in the display, as well as how the data is distributed (how many values each bar represents).

Histogram range

HRNG enables you to specify the range of values for a set of histogram bars. The range runs from the left edge of the leftmost bar to the right edge of the rightmost bar. You can limit the range to exclude any values you suspect are outliers.

Plotting mark

(2VAR)

S1MARK through S5MARK enables you to specify one of five symbols to use to plot each data set. Press to change the highlighted setting.

Connected points

(2VAR)

10-18

CONNECT (on the second page), when checkmarked, connects the data points as they are plotted. The resulting

line is not the regression curve. The order of plotting is according to the ascending order of independent values.

Statistics aplet


For instance, the data set (1,1), (3,9), (4,16), (2,4) would be plotted and traced in the order (1,1), (2,4), (3,9),

(4,16).

Trouble-shooting a plot

If you have problems plotting, check that you have the following:

• The correct view).

or menu label on (Numeric

• The correct fit (regression model), if the data set is two-variable.

• Only the data sets to compute or plot are checkmarked (Symbolic view).

• The correct plotting range. Try using Auto

Scale (instead of ), or adjust the plotting parameters (in Plot Setup) for the ranges of the axes and the width of histogram bars ( HWIDTH).

In mode, ensure that both paired columns contain data, and that they are the same length.

In mode, ensure that a paired column of frequency values is the same length as the data column that it refers to.

Exploring the graph

The Plot view has menu keys for zooming, tracing, and coordinate display. There are also scaling options under

. These options are described in“Exploring the graph” on page 2-7.

Statistics aplet’s PLOT view keys

Key Meaning

CLEAR Erases the plot.

Offers additional pre-defined views for splitting the screen, overlaying plots, and autoscaling the axes.

Moves cursor to far left or far right.



Key

(2var statistics only)


Displays ZOOM menu.

Turns trace mode on/off. The white box appears next to the option when

Trace mode is active.

Turns fit mode on or off. Turning on draws a curve to fit the data points according to the current regression model.

Enables you to specify a value on the line of best fit to jump to or a data point number to jump to.

Displays the equation of the regression curve.

Hides and displays the menu key labels. When the labels are hidden, any menu key displays the (x,y) coordinates. Pressing redisplays the menu labels.

Calculating predicted values

The functions PREDX and PREDY estimate (predict) values for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data according to the specified fit.

Find predicted values

1. In Plot view, draw the regression curve for the data set.

2. Press to move to the regression curve.

3. Press and enter the value of X. The cursor jumps to the specified point on the curve and the coordinate display shows X and the predicted value of Y.

In HOME:

• Enter PREDX(y-value) to find the predicted value for the independent variable given a hypothetical dependent value.



H I N T

• Enter PREDY(x-value) to find the predicted value of the dependent variable given a hypothetical independent variable.

You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category.

In cases where more than one fit curve is displayed, the

PREDY function uses the most recently calculated curve. In order to avoid errors with this function, uncheck all fits except the one that you want to work with, or use the Plot

View method.




11

Inference aplet

About the Inference aplet

The Inference capabilities include calculation of confidence intervals and hypothesis tests based on the

Normal Z-distribution or Student’s t-distribution.

Based on the statistics from one or two samples, you can test hypotheses and find confidence intervals for the following quantities:

• mean

• proportion

• difference between two means

• difference between two proportions

Example data

When you first access an input form for an Inference test, by default, the input form contains example data. This example data is designed to return meaningful results that relate to the test. It is useful for gaining an understanding of what the test does, and for demonstrating the test. The calculator’s on-line help provides a description of what the example data represents.

Getting started with the Inference aplet

This example describes the Inference aplet’s options and functionality by stepping you through an example using the example data for the Z-Test on 1 mean.

Open the

Inference aplet

1. Open the Inference aplet.

Select Inference

.

The Inference aplet opens in the Symbolic view.

Inference aplet 11-1


Inference aplet’s SYMB view keys

The table below summarizes the options available in

Symbolic view.

Hypothesis

Tests

Z: 1 μ, the Z-Test on 1 mean

Z: μ

1

T: μ

– μ

2

, the

Z-Test on the difference of two means

Z: 1 π, the Z-Test on 1 proportion

Z: π1 – π2, the

Z-Test on the difference in two proportions

T: 1 μ, the T-Test on

1 mean

1

– μ means

2

, the T-

Test on the difference of two

Confidence Intervals

Z-Int: 1 μ, the confidence interval for 1 mean, based on the Normal distribution

Z-Int: μ

1

– μ

2

, the confidence interval for the difference of two means, based on the

Normal distribution

Z-Int: 1 π, the confidence interval for 1 proportion, based on the Normal distribution

Z-Int: π1 – π2, the confidence interval for the difference of two proportions, based on the

Normal distribution

T-Int: 1 μ, the confidence interval for 1 mean, based on the Student’s t-distribution

T-Int: μ

1

– μ

2

, the confidence interval for the difference of two means, based on the

Student’s t-distribution

11-2

If you choose one of the hypothesis tests, you can choose the alternative hypothesis to test against the null hypothesis. For each test, there are three possible choices for an alternative hypothesis based on a quantitative comparison of two quantities. The null hypothesis is always that the two quantities are equal.Thus, the alternative hypotheses cover the various cases for the two quantities being unequal: <, >, and ≠.

In this section, we will use the example data for the Z-Test on 1 mean to illustrate how the aplet works and what features the various views present.

Inference aplet


Select the inferential method

Enter data

2. Select the Hypothesis Test inferential method.

Select HYPOTH TEST

3. Define the type of test.

Z–Test: 1 μ

4. Select an alternative hypothesis.

μ< μ0

5. Enter the sample statistics and population parameters. setup-NUM

Inference aplet

The table below lists the fields in this view for our current

Z-Test: 1 μ example.

Definition x n

α

Field name

μ0

σ

Assumed population mean

Population standard deviation

Sample mean

Sample size

Alpha level for the test

11-3


Display on-line help

By default, each field already contains a value.

These values constitute the example database and are explained in the feature of this aplet.

6. To display the on-line help, press

7. To close the on-line help, press .

Display test results in numeric format

8. Display the test results in numeric format.

The test distribution value and its associated probability are displayed, along with the critical value(s) of the test and the associated critical value(s) of the statistic.

Note: You can access the on-line help in Numeric view.

Plot test results

9. Display a graphic view of the test results.

Horizontal axes are presented for both the distribution variable and the test statistic. A generic bell curve represents the probability distribution function. Vertical lines mark the critical value(s) of the test, as well as the value of the test statistic. The rejection region is marked R and the test numeric results are displayed between the horizontal axes.

Importing sample statistics from the Statistics aplet

The Inference aplet supports the calculation of confidence intervals and the testing of hypotheses based on data in the Statistics aplet. Computed statistics for a sample of data in a column in any Statistics-based aplet can be imported for use in the Inference aplet. The following example illustrates the process.

11-4 Inference aplet


Open the


A calculator produces the following 6 random numbers:

0.529, 0.295, 0.952, 0.259, 0.925, and 0.592

1. Open the Statistics aplet and reset the current settings.

Select

Statistics

Enter data

Calculate statistics

H I N T

The Statistics aplet opens in the Numeric view.

2. In the C1 column, enter the random numbers produced by the calculator.

529

295

952

259

925

592

(

If the Decimal Mark setting in the Modes input form modes) is set to Comma, use instead of .

3. If necessary, select 1-variable statistics. Do this by pressing the fifth menu key until as its menu label.

is displayed

4. Calculate statistics.

Inference aplet

The mean of 0.592 seems a little large compared to the expected value of 0.5. To see if the difference is statistically significant, we will use the statistics computed here to construct a confidence interval for the true mean of the population of random numbers and see whether or not this interval contains 0.5.

5. Press to close the computed statistics window.

11-5


Open Inference aplet

6. Open the Inference aplet and clear current settings.

Select

Inference

Select inference method and type

7. Select an inference method.

Select CONF INTERVAL

Set up the interval calculation

8. Select a distribution statistic type.

Select T-Int: 1 μ

9. Set up the interval calculation. Note: The default values are derived from sample data from the on-line help example.

Setup-NUM



Import the data

10.Import the data from the Statistics aplet. Note: The data from C1 is displayed by default.

Note: Press to see the statistics before importing them into the

Numeric Setup view.

Also, if there is more than one aplet based on the

Statistics aplet, you are prompted to choose one.

11.Specify a 90% confidence interval in the C: field.

to move to the C: field

0.9

Display Numeric view

12.Display the confidence interval in the Numeric view.

Note: The interval setting is 0.5.

Display Plot view

13.Display the confidence interval in the Plot view.

You can see, from the second text row, that the mean is contained within the 90% confidence interval (CI) of 0.3469814 to 0.8370186.

Note: The graph is a simple, generic bell-curve. It is not meant to accurately represent the t-distribution with 5 degrees of freedom.



Hypothesis tests

You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are based on statistics of samples of the populations.

The HP 39gs hypothesis tests use the Normal

Z-distribution or Student’s t-distribution to calculate probabilities.

One-Sample Z-Test

Menu name

Z-Test: 1 μ

On the basis of statistics from a single sample, the

One-Sample Z-Test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the population mean equals a specified value Η

0

: μ = μ

0

.

You select one of the following alternative hypotheses against which to test the null hypothesis:

H

1

:μ

1

< μ

2

H

1

:μ

1

> μ

2

H

1

:μ

1

≠ μ

2

Inputs

The inputs are:

Field name x n

μ

0

σ

α

Definition

Sample mean.

Sample size.

Hypothetical population mean.

Population standard deviation.

Significance level.



Results

The results are:

Result

Test Z

Prob

Critical Z

Description

Z-test statistic.

Probability associated with the

Z-Test statistic.

Boundary values of Z associated with the α level that you supplied.

Critical x by the α value that you supplied.

Two-Sample Z-Test

Menu name

Z-Test: μ1–μ2

On the basis of two samples, each from a separate population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the mean of the two populations are equal (H

0

: μ1= μ2).


H

1

:μ

1

< μ

2

H

1

:μ

1

> μ

2

H

1

:μ

1

≠ μ

2

Inputs

The inputs are:

Field name x1 x2 n1 n2

σ1

Definition

Sample 1 mean.

Sample 2 mean.

Sample 1 size.

Sample 2 size.

Population 1 standard deviation.



Results

Field name

σ2

α

The results are:

Result

Test Z

Prob

Critical Z

Definition (Continued)


Significance level.

Description

Z-Test statistic.


Z-Test statistic.

Boundary value of Z associated with the α level that you supplied.

One-Proportion Z-Test

Menu name

Z-Test: 1π

On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the proportion of successes in the two populations is equal: H

0

: π = π

0


H

1

: π π

0

H

1

: π π

0

H

1

: π π

0



Inputs

The inputs are:

Field name Definition x Number of successes in the sample.

n

π

0

α

Sample size.

Population proportion of successes.

Significance level.

Results

The results are:

Result

Test P

Test Z

Prob

Critical Z

Description

Proportion of successes in the sample.

Z-Test statistic.

Probability associated with the Z-Test statistic.

Boundary value of Z associated with the level you supplied.

Two-Proportion Z-Test

Menu name

Z-Test: π1 – π2

On the basis of statistics from two samples, each from a different population, the Two-Proportion Z-Test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the proportion of successes in the two populations is equal

H0: π

1

= π

2

.


H

1

:π

1

<

H

1

:π

1

>

H

1

:π

1

≠

π

2

π

2

π

2



Inputs

Results

The inputs are:

Field name

X1

X2 n1 n2

α

The results are:

Result

Test π1–π2

Definition

Sample 1 mean.

Sample 2 mean.

Sample 1 size.

Sample 2 size.

Significance level.

Test Z

Prob

Critical Z

Description

Difference between the proportions of successes in the two samples.

Z-Test statistic.


Z-Test statistic.

Boundary values of Z associated with the α level that you supplied.

One-Sample T-Test

Menu name

11-12

T-Test: 1 μ

The One-sample T-Test is used when the population standard deviation is not known. On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the sample mean has some assumed value,

Η

0

:μ = μ

0


H

1

: <

0

H

1

: >

0

H

1

: ≠

0

Inference aplet


Inputs

Results

The inputs are:

Field name x

Sx n

μ0

α

The results are:

Result

Test T

Prob

Critical T

Critical x

Definition

Sample mean.

Sample standard deviation.

Sample size.

Hypothetical population mean.

Significance level.

Description

T-Test statistic.


T-Test statistic.

Boundary value of T associated with the α level that you supplied.

by the α value that you supplied.



Two-Sample T-Test

Menu name

Inputs

T-Test: μ1 – μ2

The Two-sample T-Test is used when the population standard deviation is not known. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the two populations means are equal H

0

: μ

1

= μ

2

.

You select one of the following alternative hypotheses against which to test the null hypothesis

H

1

: μ

1

H

1

: μ

1

H

1

: μ

1

< μ

2

> μ

2

≠ μ

2

The inputs are:

Field name x1

Definition

Sample 1 mean.

x2 Sample 2 mean.

S1

S2

Sample 1 standard deviation.


n1 n2

α

Sample 1 size.

Sample 2 size.

Significance level.

_Pooled?

Check this option to pool samples based on their standard deviations.



Results

The results are:

Result

Test T

Prob

Critical T

Description

T-Test statistic.

Probability associated with the T-Test statistic.

Boundary values of T associated with the α level that you supplied.

Confidence intervals

The confidence interval calculations that the HP 39gs can perform are based on the Normal Z-distribution or

Student’s t-distribution.

One-Sample Z-Interval

Menu name

Inputs

Z-INT: μ 1

This option uses the Normal Z-distribution to calculate a confidence interval for m, the true mean of a population, when the true population standard deviation, s, is known.

The inputs are: x

σ n

C

Field name

Definition

Sample mean.

Population standard deviation.

Sample size.

Confidence level.



Results

The results are:

Result

Critical Z

μ min

μ max

Description

Critical value for Z.

Lower bound for μ.

Upper bound for μ.

Two-Sample Z-Interval

Menu name

Inputs

Z-INT: μ1– μ2

This option uses the Normal Z-distribution to calculate a confidence interval for the difference between the means of two populations, μ

1 deviations, σ

1

and σ

2

– μ

2

, when the population standard

, are known.

The inputs are: x2 n1 n2

σ1

σ2

C

Field name x1

Definition

Sample 1 mean.

Sample 2 mean.

Sample 1 size.

Sample 2 size.



Confidence level.

Results

The results are:

Result Description

Critical Z Critical value for Z.

Δ μ Min Lower bound for μ

1

– μ

2

.

Δ μ Max Upper bound for μ

1

– μ

2

.



One-Proportion Z-Interval

Menu name

Inputs

Z-INT: 1 π

This option uses the Normal Z-distribution to calculate a confidence interval for the proportion of successes in a population for the case in which a sample of size, n, has a number of successes, x.

The inputs are: x n

Field name

C

Definition

Sample success count.

Sample size.

Confidence level.

Results

The results are:

Result

Critical Z

π Min

π Max

Description


Lower bound for π.

Upper bound for π.

Two-Proportion Z-Interval

Menu name Z-INT: π1 – π2

This option uses the Normal Z-distribution to calculate a confidence interval for the difference between the proportions of successes in two populations.

Inputs

The inputs are:

Definition Field name x1 x2

Sample 1 success count.

Sample 2 success count.



Results

Field name n1 n2

C

Definition (Continued)

Sample 1 size.

Sample 2 size.

Confidence level.

The results are:

Result Description

Critical Z

Δ π Min

Δ π Max


Lower bound for the difference between the proportions of successes.

Upper bound for the difference between the proportions of successes.

One-Sample T-Interval

Menu name

Inputs

T-INT: 1 μ

This option uses the Student’s t-distribution to calculate a confidence interval for m, the true mean of a population, for the case in which the true population standard deviation, s, is unknown.

The inputs are:

Sx n

C

Field name x1

Definition

Sample mean.

Sample standard deviation.

Sample size.

Confidence level.



Results

The results are:

Result

Critical T

μ Min

μ Max

Description

Critical value for T.

Lower bound for μ.

Upper bound for μ.

Two-Sample T-Interval

Menu name

Inputs

T-INT: μ1 – μ2

This option uses the Student’s t-distribution to calculate a confidence interval for the difference between the means of two populations, μ1 – μ2, when the population standard deviations, s1and s2, are unknown.

The inputs are:

Field name x1 x2 s1 s2 n1 n2

C

_Pooled

Definition

Sample 1 mean.

Sample 2 mean.



Sample 1 size.

Sample 2 size.

Confidence level.

Whether or not to pool the samples based on their standard deviations.



Results

The results are:

Result

Critical T

Δ μ Min

Δ μ Max

Description

Critical value for T.

Lower bound for μ1 – μ2.

Upper bound for μ1 – μ2.



12

Using the Finance Solver

The Finance Solver, or Finance aplet, is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows:

Press the key or the soft menu key to activate the aplet. The resulting screen shows the different elements involved in the solution of financial problems with your HP 39gs calculator.

Background information on and applications of financial calculations are provided next.

Background

Using the Finance Solver

The Finance Solver application provides you with the ability of solving time-value-of-money (TVM) and amortization problems. These problems can be used for calculations involving compound interest applications as well as amortization tables.

Compound interest is the process by which earned interest on a given principal amount is added to the principal at specified compounding periods, and then the

12-1


12-2 combined amount earns interest at a certain rate.

Financial calculations involving compound interest include savings accounts, mortgages, pension funds, leases, and annuities.

Time Value of Money (TVM) calculations, as the name implies, make use of the notion that a dollar today will be worth more than a dollar sometime in the future. A dollar today can be invested at a certain interest rate and generate a return that the same dollar in the future cannot.

This TVM principle underlies the notion of interest rates, compound interest and rates of return.

TVM transactions can be represented by using cash flow

diagrams. A cash flow diagram is a time line divided into equal segments representing the compounding periods.

Arrows represent the cash flows, which could be positive

(upward arrows) or negative (downward arrows), depending on the point of view of the lender or borrower.

The following cash flow diagram shows a loan from a

borrower's point of view:

Present value (PV)

(Loan)

Money received is a positive number

Money paid out is a negative number

Equal periods

1 2 3 4 5

Payment

(PMT)

Payment

(PMT)

Payment

(PMT)

Payment

(PMT)

Equal payments

(PMT)

Future value

(FV)

On the other hand, the following cash flow diagram shows a load from the lender's point of view:

Equal payments

FV

PMT PMT PMT PMT

PMT

Loan

} 1 2 3 4

Equal periods

5

PV

In addition, cash flow diagrams specify when payments occur relative to the compounding periods: at the

beginning of each period or at the end. The Finance

Solver application provides both of these payment modes: Begin mode and End mode. The following cash


HP 39gs English.book Page 3 Wednesday, December 7, 2005 11:24 PM flow diagram shows lease payments at the beginning of each period.

PV

}

Capitalized value of lease

1 2 3 4 5

PMT PMT PMT PMT PMT

FV

The following cash flow diagram shows deposits into an account at the end of each period.

FV

1 2 3 4 5

PMT PMT PMT PMT PMT

PV

As these cash-flow diagrams imply, there are five TVM variables:

N

I%YR

PV

The total number of compounding periods or payments.

The nominal annual interest rate (or investment rate). This rate is divided by the number of payments per year (P/YR) to compute the nominal interest rate per

compounding period -- which is the interest rate actually used in TVM calculations.

The present value of the initial cash flow.

To a lender or borrower, PV is the amount of the loan; to an investor, PV is the initial investment. PV always occurs at the beginning of the first period.

Using the Finance Solver 12-3


PMT

FV

The periodic payment amount. The payments are the same amount each period and the TVM calculation assumes that no payments are skipped. Payments can occur at the beginning or the end of each compounding period -- an option you control by setting the Payment mode to Beg or End.

The future value of the transaction: the amount of the final cash flow or the compounded value of the series of previous cash flows. For a loan, this is the size of the final balloon payment (beyond any regular payment due). For an investment this is the cash value of an investment at the end of the investment period.

Performing TVM calculations

1. Launch the Financial Solver as indicated at the beginning of this section.

2. Use the arrow keys to highlight the different fields and enter the known variables in the TVM calculations, pressing the soft-menu key after entering each known value. Be sure that values are entered for at least four of the five TVM variables (namely, N, I%YR,

PV, PMT, and FV).

3. If necessary, enter a different value for P/YR (default value is 12, i.e., monthly payments).

4. Press the key to change the Payment mode (Beg or End) as required.

5. Use the arrow keys to highlight the TVM variable you wish to solve for and press the soft-menu key.

12-4 Using the Finance Solver


Example 1 - Loan calculations

Suppose you finance the purchase of a car with a 5-year loan at 5.5% annual interest, compounded monthly. The purchase price of the car is $19,500, and the down payment is $3,000. What are the required monthly payments? What is the largest loan you can afford if your maximum monthly payment is $300? Assume that the payments start at the end of the first period.

Solution. The following cash flow diagram illustrates the loan calculations:

PV = $16,500 FV = 0 l%YR = 5.5

N = 5 x 12 = 60

P/YR = 12; End mode

1 2 59 60

PMT = ?

Start the Finance Solver, selecting P/YR = 12 and End payment option.

• Enter the known TVM variables as shown in the diagram above. Your input form should look as follows:


• Highlighting the PMT field, press the soft menu key to obtain a payment of -315.17 (i.e., PMT

= -$315.17).

• To determine the maximum loan possible if the monthly payments are only $300, type the value

–300 in the PMT field, highlight the PV field, and press the soft menu key. The resulting value is

PV = $15,705.85.

12-5


Example 2 - Mortgage with balloon payment

Suppose you have taken out a 30-year, $150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repaying the loan in a balloon payment. Find the size of the balloon payment, the value of the mortgage after 10 years of payment.

Solution. The following cash flow diagram illustrates the case of the mortgage with balloon payment:

PV = $150,000 l%YR = 6.5

N = 30 x 12 = 360 (for PMT)

N = 10 x 12 = 120 (for balloon payment)

P/YR = 12; End mode

1 2 59 60

PMT = ?

Balloon payment,

FV = ?

• Start the Finance Solver, selecting P/YR = 12 and

End payment option.

• Enter the known TVM variables as shown in the diagram above. Your input form, for calculating monthly payments for the 30-yr mortgage, should look as follows:

12-6

• Highlighting the PMT field, press the soft menu key to obtain a payment of -948.10 (i.e., PMT

= -$948.10)

• To determine the balloon payment or future value (FV) for the mortgage after 10 years, use N = 120, highlight the FV field, and press the soft menu key. The resulting value is FV = -$127,164.19. The negative value indicates a payment from the homeowner. Check that the required balloon payments at the end of 20 years (N=240) and 25 years (N = 300) are -$83,497.92 and

-$48,456.24, respectively.



Calculating Amortizations

Amortization calculations, which also use the TVM variables, determine the amounts applied towards principal and interest in a payment or series of payments.

To calculate amortizations:

1. Start the Finance Solver as indicated at the beginning of this section.

2. Set the following TVM variables: a Number of payments per year (P/YR) b Payment at beginning or end of periods

3. Store values for the TVM variables I%YR, PV, PMT, and FV, which define the payment schedule.

4. Press the soft menu key and enter the number of payments to amortize in this batch.

5. Press the soft menu key to amortize a batch of payments. The calculator will provide for you the amount applied to interest, to principal, and the remaining balance after this set of payments have been amortized.

Example 3 - Amortization for home mortgage

For the data of Example 2 above, find the amortization of the loan after the first 10 years (12x10 = 120 payments).

Pressing the soft menu key produces the screen to the left. Enter 120 in the PAYMENTS field, and press the soft menu key to produce the results shown to the right.

To continue amortizing the loan:

1. Press the soft menu key to store the new balance after the previous amortization as PV.

2. Enter the number of payments to amortize in the new batch.

Using the Finance Solver 12-7


3. Press the soft menu key to amortize the new batch of payments. Repeat steps 1 through 3 as often as needed.

Example 4 - Amortization for home mortgage

For the results of Example 3, show the amortization of the next 10 years of the mortgage loan. First, press the soft menu key. Then, keeping 120 in the PAYMENTS field, press the shown below.

soft menu key to produce the results

To amortize a series of future payments starting at payment p:

1. Calculate the balance of the loan at payment p-1.

2. Store the new balance in PV using the menu key.

soft

3. Amortize the series of payments starting at the new

PV.

The amortization operation reads the values from the

TVM variables, rounds the numbers it gets from PV and

PMT to the current display mode, then calculates the amortization rounded to the same setting. The original variables are not changed, except for PV, which is updated after each amortization.

12-8 Using the Finance Solver


13

Using mathematical functions

Math functions

The HP 39gs contains many math functions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices.

The Probability category (shown as Prob. on the MATH menu) contains functions for working with probability.

To use a math function, you enter the function onto the command line, and include the arguments in parentheses after the function. You can also select a math function from the MATH menu.

The MATH menu

The MATH menu provides access to math functions, physical constants, and programming constants.

The MATH menu is organized by category. For each category of functions on the left, there is a list of function names on the right. The highlighted category is the current category.

• When you press , you see the menu list of

Math categories in the left column and the corresponding functions of the highlighted category in the right column. The menu key indicates that the MATH FUNCTIONS menu list is active.

To select a function

1. Press to display the MATH menu. The categories appear in alphabetical order. Press or

to scroll through the categories. To skip directly to a category, press the first letter of the category’s name. Note: You do not need to press first.

Using mathematical functions 13-1


2. The list of functions (on the right) applies to the currently highlighted category (on the left). Use and to switch between the category list and the function list.

3. Highlight the name of the function you want and press . This copies the function name (and an initial parenthesis, if appropriate) to the edit line.

Function categories

• Calculus

• Complex numbers

• Constant

• Convert

• Hyperbolic trigonometry

(Hyperb.)

• Lists

• Loop

• Matrix

• Polynomial

• Probability

• Real numbers

(Real)

• Two-variable statistics

(Stat-Two)

• Symbolic

• Tests

• Trigonometry

(Trig)

Math functions by category

Syntax

Each function’s definition includes its syntax, that is, the exact order and spelling of a function’s name, its delimiters (punctuation), and its arguments. Note that the syntax for a function does not require spaces.

Functions common to keyboard and menus

These functions are common to the keyboard and MATH menu.

π

ARG

For a description, see “π” on page 13-8.

For a description, see “ARG” on page 13-7.

13-2

AND page 11-7.

For a description, see “AND” on page 13-19.

Using mathematical functions


!

∑

EEX

For a description, see

“COMB(5,2) returns 10. That is, there are ten different ways that five things can be combined two at a time.!” on page 13-12.

For a description, see “Σ” on page 13-11.

For a description, see “Scientific notation (powers of 10)” on page 1-20.

∫ x

– 1 page 11-7.

The multiplicative inverse function finds the inverse of a square matrix, and the multiplicative inverse of a real or complex number. Also works on a list containing only these object types.

Keyboard functions

The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments.

, , , Add, Subtract, Multiply, Divide. Also accepts complex numbers, lists and matrices.

value1+ value2, etc.

e x

Natural exponential. Also accepts complex numbers.

e^value

Example e^5 returns 148.413159103

Natural logarithm. Also accepts complex numbers.

LN(value)

Example

LN(1) returns 0



13-4

10 x

, ,

ASIN

ACOS

Exponential (antilogarithm). Also accepts complex numbers.

10^value

Example

10^3 returns 1000

Common logarithm. Also accepts complex numbers.

LOG(value)

Example

LOG(100) returns 2

Sine, cosine, tangent. Inputs and outputs depend on the current angle format (Degrees, Radians, or Grads).

SIN(value)

COS(value)

TAN(value)

Example

TAN(45) returns 1 (Degrees mode).

Arc sine: sin

–1

x. Output range is from –90° to 90°, –π/2 to π/2, or –100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers.

ASIN(value)

Example

ASIN(1) returns 90 (Degrees mode).

Arc cosine: cos

–1

x. Output range is from 0° to 180°, 0 to

π, or 0 to 200 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers.

Output will be complex for values outside the normal

COS domain of – 1 x 1 .

ACOS(value)

Example

ACOS(1) returns 0 (Degrees mode).



ATAN

ABS


Arc tangent: tan

–1

x. Output range is from –90° to 90°,

2π/2 to π/2, or –100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers.

ATAN(value)

Example

ATAN(1) returns 45 (Degrees mode).

Square. Also accepts complex numbers.

value

2

Example

18

2

returns 324

Square root. Also accepts complex numbers.

value

Example

324 returns 18

Negation. Also accepts complex numbers.

–value

Example

-(1,2) returns (-1,-2)

Power (x raised to y). Also accepts complex numbers.

value^power

Example

2^8 returns 256

Absolute value. For a complex number, this is

ABS(value)

ABS((x,y)) x

2

+ y

2

.

Example

ABS(–1) returns 1

ABS((1,2)) returns 2.2360679775

13-5

HP 39gs English.book Page 6 Wednesday, December 7, 2005 11:24 PM n root NTHROOT value

Example

3 NTHROOT 8 returns 2

∫

Calculus functions

The symbols for differentiation and integration are available directly form the keyboard— and S respectively—as well as from the MATH menu.

∂ Differentiates expression with respect to the variable of differentiation. From the command line, use a formal

name (S1, etc.) for a non-numeric result. See “Finding derivatives” on page 13-21.

∂ variable(expression)

Example

∂ s1(s1

2

+3*s1) returns 2*s1+3

Integrates expression from lower to upper limits with respect to the variable of integration. To find the definite integral, both limits must have numeric values (that is, be numbers or real variables). To find the indefinite integral, one of the limits must be a formal variable (s1, etc).

∫ (lower, upper, expression, variable)

See “Using formal variables” on page 13-20 for

further details.

Example

∫ (0,s1,2*X+3,X) finds the indefinite result 3*s1+2*(s1^2/2)

See “To find the indefinite integral using formal variables” on page 13-23 for more information on

finding indefinite integrals.

13-6 Using mathematical functions


TAYLOR

Calculates the nth order Taylor polynomial of expression at the point where the given variable = 0.

TAYLOR (expression, variable, n)

Example

TAYLOR(1 + sin(s1)

2

,s1,5)with Radians angle measure and Fraction number format (set in

MODES) returns 1+s1^2-1/3*s1^4.

Complex number functions

These functions are for complex numbers only. You can also use complex numbers with all trigonometric and hyperbolic functions, and with some real-number and keyboard functions. Enter complex numbers in the form

(x,y), where x is the real part and y is the imaginary part.

ARG

Argument. Finds the angle defined by a complex number.

Inputs and outputs use the current angle format set in

Modes.

ARG((x, y))

Example

ARG((3,3)) returns 45 (Degrees mode)

CONJ

Complex conjugate. Conjugation is the negation (sign reversal) of the imaginary part of a complex number.

CONJ((x, y))

Example

CONJ((3,4)) returns (3,-4)

IM

Imaginary part, y, of a complex number, (x, y).

IM ((x, y))

Example

IM((3,4)) returns 4

RE

Real part x, of a complex number, (x, y).

RE((x, y))

Example

RE((3,4)) returns 3



Constants

e i

MAXREAL

MINREAL

π

Conversions

The constants available from the MATH FUNCTIONS menu are mathematical constants. These are described in this section. The hp 39gs has two other menus of constants: program constants and physical constants.

These are described in “Program constants and physical constants” on page 13-24.

Natural logarithm base. Internally represented as

2.71828182846.

e

Imaginary value for i

– 1 , the complex number (0,1).

Maximum real number. Internally represented as

9.99999999999 x 10

499

.

MAXREAL

Minimum real number. Internally represented as

1 x10

-499

.

MINREAL

Internally represented as 3.14159265359.

π

→C

→F

→CM

13-8

The conversion functions are found on the Convert menu. They enable you to make the following conversions.

Convert from Fahrenheit to Celcius.

Example

→C(212) returns 100

Convert from Celcius to Fahrenheit.

Example

→F(0) returns 32

Convert from inches to centimeters.



→IN

→L

→LGAL

→KG

→LBS

→KM

→MILE

→DEG

→RAD

Convert from centimeters to inches.

Convert from US gallons to liters.

Convert from liters to US gallons.

Convert from pounds to kilograms.

Convert from kilograms to pounds.

Convert from miles to kilometers.

Convert from kilometers to miles.

Convert from radians to degrees.

Convert from degrees to radians.

Hyperbolic trigonometry

The hyperbolic trigonometry functions can also take complex numbers as arguments.

ACOSH

ASINH

ATANH

Inverse hyperbolic cosine : cosh

–1 x.

ACOSH(value)

Inverse hyperbolic sine : sinh

–1

x.

ASINH(value)

Inverse hyperbolic tangent : tanh

–1 x.

ATANH(value)

COSH

Hyperbolic cosine

COSH(value)

SINH

Hyperbolic sine.

SINH(value)

TANH

Hyperbolic tangent.

TANH(value)

ALOG

Antilogarithm (exponential). This is more accurate than

10^x due to limitations of the power function.

ALOG(value)



EXP

EXPM1

LNP1

Natural exponential. This is more accurate than e x

due to limitations of the power function.

EXP(value)

Exponent minus 1 : e x

– 1 . This is more accurate than

EXP when x is close to zero.

EXPM1(value)

Natural log plus 1 : ln(x+1). This is more accurate than the natural logarithm function when x is close to zero.

LNP1(value)

List functions

These functions work on list data. See “List functions” on page 16-6.

Loop functions

ITERATE

RECURSE

The loop functions display a result after evaluating an expression a given number of times.

Repeatedly for #times evaluates an expression in terms of

variable. The value for variable is updated each time, starting with initialvalue.

ITERATE(expression, variable, initialvalue,

#times )

Example

ITERATE(X

2

,X,2,3) returns 256

Provides a method of defining a sequence without using the Symbolic view of the Sequence aplet. If used with |

(“where”), RECURSE will step through the evaluation.

RECURSE(sequencename, term n

, term

1

, term

2

)

Example

RECURSE(U,U(N-1)*N,1,2) U1(N)

Stores a factorial-calculating function named U1.

When you enter U1(5), for example, the function calculates 5! (120).



Σ Summation. Finds the sum of expression with respect to

variable from initialvalue to finalvalue.

Σ(variable=initialvalue, finalvalue, expression)

Example

Σ(C=1,5,C 2

) returns 55.

Matrix functions

These functions are for matrix data stored in matrix

variables. See “Matrix functions and commands” on page 15-10.

Polynomial functions

Polynomials are products of constants (coefficients) and variables raised to powers (terms).

POLYCOEF

Polynomial coefficients. Returns the coefficients of the polynomial with the specified roots.

POLYCOEF ([roots])

Example

To find the polynomial with roots 2, –3, 4, –5:

POLYCOEF([2,-3,4,-5]) returns[1,2,-25,

-26,120], representing x

4

+2x

3

–25x

2

–26x+120.

POLYEVAL

Polynomial evaluation. Evaluates a polynomial with the specified coefficients for the value of x.

POLYEVAL([coefficients], value)

Example

For x

4

+2x

3

–25x

2

–26x+120:

POLYEVAL([1,2,-25,-26,120],8) returns

3432.

POLYFORM

Polynomial form. Creates a polynomial in variable1 from expression.

POLYFORM(expression, variable1)

Example

POLYFORM((X+1)^2+1,X) returns X^2+2*X+2.



POLYROOT

H I N T

Polynomial roots. Returns the roots for the nth-order polynomial with the specified n+1 coefficients.

POLYROOT([coefficients])

Example

For x

4

+2x

3

–25x

2

–26x+120:

POLYROOT([1,2,-25,-26,120]) returns

[2,-3,4,-5].

The results of POLYROOT will often not be easily seen in

HOME due to the number of decimal places, especially if they are complex numbers. It is better to store the results of POLYROOT to a matrix.

For example, POLYROOT([1,0,0,-8] M1 will store the three complex cube roots of 8 to matrix M1 as a complex vector. Then you can see them easily by going to the Matrix Catalog. and access them individually in calculations by referring to M1(1), M1(2) etc.

Probability functions

COMB

PERM

Number of combinations (without regard to order) of n things taken r at a time: n!/(r!(n-r)).

COMB(n, r)

Example

COMB(5,2) returns 10. That is, there are ten different ways that five things can be combined two at a time.!

Factorial of a positive integer. For non-integers, ! = Γ(x +

1). This calculates the gamma function.

value!

Number of permutations (with regard to order) of n things taken r at a time: n!/(r!(n-r)!

PERM (n, r)

Example

PERM(5,2) returns 20. That is, there are 20 different permutations of five things taken two at a time.



RANDOM

H I N T

Random number (between zero and 1). Produced by a pseudo-random number sequence. The algorithm used in the RANDOM function uses a seed number to begin its sequence. To ensure that two calculators must produce different results for the RANDOM function, use the

RANDSEED function to seed different starting values before using RANDOM to produce the numbers.

RANDOM

The setting of Time will be different for each calculator, so using RANDSEED(Time) is guaranteed to produce a set of numbers which are as close to random as possible. You can set the seed using the command RANDSEED.

UTPC

UTPF

UTPN

UTPT

Upper-Tail Chi-Squared Probability given degrees of freedom, evaluated at value. Returns the probability that a χ

2

random variable is greater than value.

UTPC(degrees, value)

Upper-Tail Snedecor’s F Probability given numerator degrees of freedom and denominator degrees of freedom

(of the F distribution), evaluated at value. Returns the probability that a Snedecor's F random variable is greater than value.

UTPF(numerator, denominator, value)

Upper-Tail Normal Probability given mean and variance, evaluated at value. Returns the probability that a normal random variable is greater than value for a normal distribution. Note: The variance is the square of the

standard deviation.

UTPN(mean, variance, value)

Upper-Tail Student’s t-Probability given degrees of freedom, evaluated at value. Returns the probability that the Student's t- random variable is greater than value.

UTPT(degrees, value)

Real-number functions

Some real-number functions can also take complex arguments.

CEILING

Smallest integer greater than or equal to value.

CEILING(value)



DEG

→

RAD

FLOOR

FNROOT

FRAC

HMS

→

→

HMS

13-14

Examples

CEILING(3.2) returns 4

CEILING(-3.2) returns -3

Degrees to radians. Converts value from Degrees angle format to Radians angle format.

DEG→RAD(value)

Example

DEG→RAD(180) returns 3.14159265359, the value of π.

Greatest integer less than or equal to value.

FLOOR(value)

Example

FLOOR(-3.2) returns -4

Function root-finder (like the Solve aplet). Finds the value for the given variable at which expression most nearly evaluates to zero. Uses guess as initial estimate.

FNROOT(expression, variable, guess)

Example

FNROOT(M*9.8/600-1,M,1) returns

61.2244897959.

Fractional part.

FRAC(value)

Example

FRAC (23.2) returns .2

Hours-minutes-seconds to decimal. Converts a number or expression in H.MMSSs format (time or angle that can include fractions of a second) to x.x format (number of hours or degrees with a decimal fraction).

HMS→(H.MMSSs)

Example

HMS→(8.30) returns 8.5

Decimal to hours-minutes-seconds. Converts a number or expression in x.x format (number of hours or degrees



INT

MANT

MAX

MIN

MOD

%

%CHANGE

Using mathematical functions with a decimal fraction) to H.MMSSs format (time or angle up to fractions of a second).

→HMS(x.x)

Example

→HMS(8.5) returns 8.3

Integer part.

INT(value)

Example

INT(23.2) returns 23

Mantissa (significant digits) of value.

MANT(value)

Example

MANT(21.2E34) returns 2.12

Maximum. The greater of two values.

MAX(value1, value2)

Example

MAX(210,25) returns 210

Minimum. The lesser of two values.

MIN(value1, value2)

Example

MIN(210,25) returns 25

Modulo. The remainder of value1/value2.

value1 MOD value2

Example

9 MOD 4 returns 1

x percent of y; that is, x/100*y.

% (x, y)

Example

% (20,50) returns 10

Percent change from x to y, that is, 100(y–x)/x.

% CHANGE(x, y)

13-15


%TOTAL

RAD→DEG

ROUND

SIGN

TRUNCATE

13-16

Example

% CHANGE(20,50) returns 150

Percent total : (100) y/x. What percentage of x, is y.

% TOTAL(x, y)

Example

% TOTAL(20,50) returns 250

Radians to degrees. Converts value from radians to degrees.

RAD→DEG (value)

Example

RAD→DEG(π) returns 180

Rounds value to decimal places. Accepts complex numbers.

ROUND(value, places)

Round can also round to a number of significant digits as showed in example 2.

Examples

ROUND(7.8676,2) returns 7.87

ROUND (0.0036757,-3) returns 0.00368

Sign of value. If positive, the result is 1. If negative, –1. If zero, result is zero. For a complex number, this is the unit vector in the direction of the number.

SIGN(value)

SIGN((x, y))

Examples

SIGN (–2) returns –1

SIGN((3,4)) returns (.6,.8)

Truncates value to decimal places. Accepts complex numbers.

TRUNCATE(value, places)

Example

TRUNCATE(2.3678,2) returns 2.36



XPON

Exponent of value.

XPON(value)

Example

XPON(123.4) returns 2

Two-variable statistics

These are functions for use with two-variable statistics.

See “Two-variable” on page 10-15.

Symbolic functions

The symbolic functions are used for symbolic manipulations of expressions. The variables can be formal or numeric, but the result is usually in symbolic

( form (not a number). You will find the symbols for the symbolic functions = and | (where) in the CHARS menu

CHARS ) as well as the MATH menu.

= ( equals )

Sets an equality for an equation. This is not a logical

operator and does not store values. (See “Test functions” on page 13-18.)

expression1=expression2

ISOLATE

Isolates the first occurrence of variable in expression=0 and returns a new expression, where

variable=newexpression. The result is a general solution that represents multiple solutions by including the (formal) variables S1 to represent any sign and n1 to represent any integer.

ISOLATE(expression, variable)

Examples

ISOLATE(2*X+8,X) returns -4

ISOLATE(A+B*X/C,X) returns -(A*C/B)

LINEAR?

Tests whether expression is linear for the specified

variable. Returns 0 (false) or 1 (true).

LINEAR?(expression, variable)

Example

LINEAR?((X^2-1)/(X+1),X) returns 0



QUAD

QUOTE

| ( where )

Solves quadratic expression= 0 for variable and returns a new expression, where variable=newexpression. The result is a general solution that represents both positive and negative solutions by including the formal variable

S1 to represent any sign: + or – .

QUAD(expression, variable)

Example

QUAD((X-1)

2

-7,X) returns

(2+s1*5.29150262213)/2

Encloses an expression that should not be evaluated numerically.

QUOTE(expression)

Examples

QUOTE(SIN(45)) F1(X) stores the expression SIN(45) rather than the value of SIN(45).

Another method is to enclose the expression in single quotes.

For example, X^3+2*X F1(X) puts the expression X^3+2*X into F1(X) in the Function aplet.

Evaluates expression where each given variable is set to the given value. Defines numeric evaluation of a symbolic expression.

expression|(variable1=value1, variable2=value2,...)

Example

3*(X+1)|(X=3) returns 12.

<

Test functions

≤

13-18

The test functions are logical operators that always return either a 1 (true) or a 0 (false).

Less than. Returns 1 if true, 0 if false.

value1<value2

Less than or equal to. Returns 1 if true, 0 if false.

value1≤value2



= =

≠

>

≥

AND

IFTE

NOT

OR

XOR

Equals (logical test). Returns 1 if true, 0 if false.

value1==value2

Not equal to. Returns 1 if true, 0 if false.

value1≠value2

Greater than. Returns 1 if true, 0 if false.

value1>value2

Greater than or equal to. Returns 1 if true, 0 if false.

value1≥value2

Compares value1 and value2. Returns 1 if they are both non-zero, otherwise returns 0.

value1 AND value2

If expression is true, do the trueclause; if not, do the falseclause.

IFTE(expression, trueclause, falseclause)

Example

IFTE(X>0,X

2

,X

3

)

Returns 1 if value is zero, otherwise returns 0.

NOT value

Returns 1 if either value1 or value2 is non-zero, otherwise returns 0. value1 OR value2

Exclusive OR. Returns 1 if either value1 or value2—but not both of them—is non-zero, otherwise returns 0.

value1 XOR value2

Trigonometry functions

The trigonometry functions can also take complex numbers as arguments. For SIN, COS, TAN, ASIN,

ACOS, and ATAN, see the Keyboard category.

ACOT

Arc cotangent.

ACOT(value)



ACSC

ASEC

COT

CSC

SEC

Arc cosecant.

ACSC(value)

Arc secant.

ASEC(value)

Cotangent: cosx/sinx.

COT(value)

Cosecant: 1/sinx

CSC(value)

Secant: 1/cosx.

SEC(value)

Symbolic calculations

The HP 39gs has the ability to perform symbolic calculations, for example, symbolic integration and differentiation. You can perform symbolic calculations in

HOME and in the Function aplet.

In HOME

When you perform calculations that contain normal variables, the calculator substitutes values for any variables. For example, if you enter A+B on the command line and press , the calculator retrieves the values for A and B from memory and substitutes them in the calculation.

Using formal variables

To perform symbolic calculations, for example symbolic differentiations and integrations, you need to use formal names. The HP 39gs has six formal names available for use in symbolic calculations. These are S0 to S5. When you perform a calculation that contains a formal name, the HP 39gs does not carry out any substitutions.

You can mix formal names and real variables. Evaluating

(A+B+S1)

2

will evaluate A+B, but not S1.

If you need to evaluate an expression that contains formal names numerically, you use the | (where) command, listed in the Math menu under the Symbolic category.

For example to evaluate (S1*S2)

2 when S1=2 and

S2=4, you would enter the calculation as follows:



(The | symbol is in the CHARS menu: press CHARS .

The = sign is listed in the MATH menu under Symbolic functions.)

Symbolic calculations in the Function aplet

You can perform symbolic operations in the Function aplet’s Symbolic view. For example, to find the derivative of a function in the Function aplet’s Symbolic view, you define two functions and define the second function as a derivative of the first function. You then evaluate the

second function. See “To find derivatives in the Function aplet’s Symbolic view” on page 13-22 for an example.

Finding derivatives

The HP 39gs can perform symbolic differentiation on some functions. There are two ways of using the HP 39gs to find derivatives.

• You can perform differentiations in HOME by using the formal variables, S1 to S5.

• You can perform differentiations of functions of X in the Function aplet.

To find derivatives in HOME

To find the derivative of the function in HOME, use a formal variable in place of X. If you use X, the differentiation function substitutes the value that X holds, and returns a numeric result.

For example, consider the function: dx ( sin ( x

2

) + 2 cos

1. Enter the differentiation function onto the command line, substituting S1 in place of X.

S1

S1

2



S1

2. Evaluate the function.

3. Show the result.

To find derivatives in the Function aplet’s Symbolic view

To find the derivative of the function in the Function aplet’s

Symbolic view, you define two functions and define the second function as a derivative of the first function. For example, to differentiate sin ( ) + 2 cos x :

1. Access the Function aplet’s Symbolic view and define

F1.

2

2. Define F2( X) as the derivative of F(1).

F1

3. Select F2( X) and evaluate it.



4. Press to display the result. Note: Use the arrow keys to view the entire function.

|

To find the indefinite integral using formal variables

You could also just define

F1 x = d x ( sin

2 cos ) .

For example, to find the indefinite integral of

∫

3x

2

∫

(

0 ,

– 5 d x

S 1 , 3 X 2

use:

− 5 , X

)

1. Enter the function.

0

X 5

X

2. Show the result format.

3. Press to close the show window.

4. Copy the result and evaluate.


Thus, substituting X for S1, it can be seen that:

∫

3x

2

– 5 d x = – 5x + 3

⎜

⎜

⎛

⎜

⎝

---------------

∂

∂

X x

3

X

⎟

⎟

⎞

⎟

⎠

13-23


This result is derived from substituting X=S1 and X=0 into the original expression found in step 1. However, substituting X=0 will not always evaluate to zero and may result in an unwanted constant.

To see this, consider:

∫

( )

4 d x =

( x –

5

2 )

5

-------------------

The ‘extra’ constant of 6.4 results from the substitution of

(x – 2)

5 x = 0 into

/5, and should be disregarded if an

indefinite integral is required.

Program constants and physical constants

When you press , three menus of functions and constants become available:

• the math functions menu (which appears by default)

• the program constants menu, and

• the physical constants menu.

The math functions menu is described extensively earlier in this chapter.

Program constants

The program constants are numbers that have been assigned to various calculator settings to enable you to test for or specify such a setting in a program. For example, the various display formats are assigned the following numbers:

1 Standard

2 Fixed

3 Scientific

4 Engineering

5 Fraction

6 Mixed fraction

In a program, you could store the constant number of a particular format into a variable and then subsequently test for that particular format.



To access the menu of program constants:

1. Press .

2. Press .

3. Use the arrow keys to navigate through the options.

4. Click and then to display the number assigned to the option you selected in the previous step.

The use of program constants is illustrated in more detail

in “Programming” on page 18-1

Physical constants

There are 29 physical constants—from the fields of chemistry, physics and quantum mechanics—that you can use in calculations. A list of all these constants can be

found in “Physical Constants” on page R-16.

To access the menu of physical constants:

1. Press .

2. Press .

3. Use the arrow keys to navigate through the options.

4. To see the symbol and value of a selected constant, press . (Click to close the information window that appears.)

The following example shows the information available about the speed of light (one of the physics constants).


5. To use the selected constant in a calculation, press

. The constant appears at the position of the cursor on the edit line.

13-25


Example

Suppose you want to know the potential energy of a mass of 5 units according to the equation E = mc

2

.

1. Enter 5

2. Press and then press .

3. Select light s...from the Physics menu.

4. Press . The menu closes and the value of the selected constant is copied to the edit line.

5. Complete the equation as you would normally and press to get the result.



14

Variables and memory management

Introduction

The HP 39gs has approximately 200K of user memory.

The calculator uses this memory to store variables, perform computations, and store history.

A variable is an object that you create in memory to hold data. The hp 39gs has two types of variables, home variables and aplet variables.

• Home variables are available in all aplets. For example, you can store real numbers in variables A to Z and complex numbers in variables Z0 to Z9.

These can be numbers you have entered, or the results of calculations. These variables are available within all aplets and within any programs.

• Aplet variables apply only to a single aplet. Aplets have specific variables allocated to them which vary from aplet to aplet.

You use the calculator’s memory to store the following objects:

• copies of aplets with specific configurations

• new aplets that you download

• aplet variables

• home variables

• variables created through a catalog or editor, for example a matrix or a text note

• programs that you create.

You can use the Memory Manager ( MEMORY ) to view the amount of memory available. The catalog views, which are accessible via the Memory Manager, can be used to transfer variables such as lists or matrices between calculators.

Variables and memory management 14-1


Storing and recalling variables

You can store numbers or expressions from a previous input or result into variables.

Numeric Precision

A number stored in a variable is always stored as a 12digit mantissa with a 3-digit exponent. Numeric precision in the display, however, depends on the display mode

(Standard, Fixed, Scientific, Engineering, or Fraction). A displayed number has only the precision that is displayed. If you copy it from the HOME view display history, you obtain only the precision displayed, not the full internal precision. On the other hand, the variable

Ans always contains the most recent result to full precision.

To store a value

1. On the command line, enter the value or the calculation for the result you wish to store.

2. Press

3. Enter a name for the variable.

4. Press .

To store the results of a calculation

If the value you want to store is in the HOME view display history, for example the results of a previous calculation, you need to copy it to the command line, then store it.

1. Perform the calculation for the result you want to store.

3 8 6

3

2. Move the highlight to the result you wish to store.

3. Press to copy the result to the command line.

4. Press .

14-2 Variables and memory management


To recall a value

5. Enter a name for the variable.

A

6. Press to store the result.

The results of a calculation can also be stored directly to a variable. For example:

2 5 3

B

To recall a variable’s value, type the name of the variable and press .

A

To use variables in calculations

You can use variables in calculations. The calculator substitutes the variable’s value in the calculation:

65 A

To clear a variable

You can use the CLRVAR command to clear a specified variable. For example, if you have stored {1,2,3,4} in variable

L1, entering CLRVAR L1

will clear L1. (You can find the

CLRVAR

command by pressing category of commands.)

and choosing the

PROMPT



The VARS menu

You use the VARS menu to access all variables in the calculator. The VARS menu is organised by category. For each variable category in the left column, there is a list of variables in the right column. You select a variable category and then select a variable in the category.

1. Open the VARS menu.

2. Use the arrow keys or press the alpha key of the first letter in the category to select a variable category.

For example, to select the Matrix category, press .

Note: In this instance, there is no need to press the ALPHA key.

3. Move the highlight to the variables column.

4. Use the arrow keys to select the variable that you want. For example, to select M2, press .



5. Choose whether to place the variable name or the variable value on the command line.

– Press to indicate that you want the variable’s contents to appear on the command line.

– Press to indicate that you want the variable’s name to appear on the command line.

6. Press to place the value or name on the command line. The selected object appears on the command line.

Example

Note: The VARS menu can also be used to enter the names or values of variables into programs.

This example demonstrates how to use the VARS menu to add the contents of two list variables, and to store the result in another list variable.

1. Display the List Catalog.

LIST to select L1

2. Enter the data for L1.

88 90 89

65 70

3. Return to the List Catalog to create L2.

LIST

to select L2



4. Enter data for L2.

55 48 86

90 77

5. Press to access HOME.

6. Open the variable menu and select L1.

7. Copy it to the command line. Note: Because the

option is highlighted, the variable’s name, rather than its contents, is copied to the command

line.

14-6

8. Insert the + operator and select the L2 variable from the List variables.

9. Store the answer in the List catalog L3 variable.

L3

Note: You can also type list names directly from the keyboard.

Variables and memory management


Home variables

It is not possible to store data of one type in a variable of another type. For example, you use the Matrix catalog to create matrices. You can create up to ten matrices, and you can store these in variables M0 to M9. You cannot store matrices in variables other than M0 to M9.

Category

Available names

Complex Z0 to Z9

For example, (1,2) Z0 or 2+3i

Z1. You can enter a complex number by typing (r,i), where r represents the real part, and i represents the imaginary part.

Graphic G0 to G9

See“Graphic commands” on page 18-21

for more information on storing graphic objects via programming commands. See

“To store into a graphics variable” on page 17-5 for more information on

storing graphic object via the sketch view.

Library

List

Aplet library variables can store aplets that you have created, either by saving a copy of a standard aplet, or downloading an aplet from another source.

L0 to L9

For example, {1,2,3} L1.

Matrix M0 to M9 can store matrices or vectors.

For example, [[1,2],[3,4]] M0.

Modes Modes variables store the modes settings that you can configure using

MODES .

Notepad Notepad variables store notes.

Program Program variables store programs.

Real A to Z and θ.

For example, 7.45 A.



Aplet variables

Most aplet variables store values that are unique to a particular aplet. These include symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections.

See the Reference Information chapter for more information about aplet variables.

Category Available names

Function F0 to F9 (Symbolic view). See “Function aplet variables” on page R-7.

Parametric X0, Y0 to X9, Y9 (Symbolic view). See

“Parametric aplet variables” on page

R-8.

Polar R0 to R9 (Symbolic view). See “Polar aplet variables” on page R-9.

Sequence U0 to U9 (Symbolic view). See

“Sequence aplet variables” on page

R-10.

Solve

Statistics

E0 to E9 (Symbolic view). See “Solve aplet variables” on page R-11.

C0 to C9 (Numeric view). See

“Statistics aplet variables” on page

R-12.

To access an aplet variable

1. Open the aplet that contains the variable you want to recall.

2. Press to display the VARS menu.

3. Use the arrow keys to select a variable category in the left column, then press to access the variables in the right column.

4. Use the arrow keys to select a variable in the right column.

5. To copy the name of the variable onto the edit line, press . ( is the default setting.)



6. To copy the value of the variable into the edit line, press press .

and

Memory Manager

You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the

Memory Manager to determine which aplets or variables consume large amounts of memory. You can make deletions to free up memory.

Example 1. Start the Memory Manager. A list of variable categories is displayed.

MEMORY

Free memory is displayed in the top right corner and the body of the screen lists each category, the memory it uses, and the percentage of the total memory it uses.

2. Select the category with which you want to work and press . Memory Manager displays memory details of variables within the category.

3. To delete variables in a category:

– Press to delete the selected variable.

– Press CLEAR to delete all variables in the selected category.




15

Matrices

Introduction

Vectors

Matrices

Matrix Variables

You can perform matrix calculations in HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas. For example, the following matrix:

1 2 3

4 5 6 is displayed in the history as:

[[1,2,3],[4,5,6]]

(If the Decimal Mark mode is set to Comma, then separate each element and each row with a period.)

You can enter matrices directly in the command line, or create them in the matrix editor.

Vectors are one-dimensional arrays. They are composed of just one row. A vector is represented with single brackets; for example, [1,2,3]. A vector can be a real number vector or a complex number vector, for example

[(1,2), (7,3)].

Matrices are two-dimensional arrays. They are composed of more than one row and more than one column.

Two-dimensional matrices are represented with nested brackets; for example, [[1,2,3],[4,5,6]]. You can create complex matrices, for example, [[(1,2), (3,4)], [(4,5),

(6,7)]].

There are ten matrix variables available, named M0 to

M9. You can use them in calculations in HOME or in a program. You can retrieve the matrix names from the

VARS menu, or just type their names from the keyboard.

Matrices 15-1


Creating and storing matrices

You can create, edit, delete, send, and receive matrices in the Matrix catalog.

To open the Matrix catalog, press MATRIX .

You can also create and store matrices—named or unnamed—-in HOME. For example, the command:

POLYROOT([1,0,–1,0]) M1 stores the root of the complex vector of length 3 into the

M1 variable. M1 now contains the three roots of x – x = 0

Matrix Catalog keys

The table below lists the operations of the menu keys in the Matrix Catalog, as well as the use of Delete ( ) and Clear ( CLEAR ).

Key Meaning

Opens the highlighted matrix for editing.

Prompts for a matrix type, then opens an empty matrix with the highlighted name.

Transmits the highlighted matrix to another hp 39gs or a disk drive.

See “Sending and receiving aplets” on page 19-4.

Receives a matrix from another hp 39gs or a disk drive. See

“Sending and receiving aplets” on page 19-4.

Clears the highlighted matrix.

CLEAR Clears all matrices.

or Moves to the end or the beginning of the catalog.

15-2 Matrices


To create a matrix in the Matrix

Catalog

1. Press MATRIX to open the Matrix Catalog. The

Matrix catalog lists the 10 available matrix variables,

M0 to M9.

2. Highlight the matrix variable name you want to use and press .

3. Select the type of matrix to create.

– For a vector (one-dimensional array), select Real vector or Complex vector.

Certain operations (+, –, CROSS) do not recognize a one-dimensional matrix as a vector, so this selection is important.

– For a matrix (two-dimensional array), select Real matrix or Complex matrix.

4. For each element in the matrix, type a number or an expression, and press . (The expression may not contain symbolic variable names.)

For complex numbers, enter each number in complex form; that is, (a, b), where a is the real part and b is the imaginary part. You must include the parentheses and the comma.

5. Use the cursor keys to move to a different row or column. You can change the direction of the highlight bar by pressing . The menu key toggles between the following three options:

– specifies that the cursor moves to the cell below the current cell when you press .

–

–

specifies that the cursor moves to the cell to the right of the current cell when you press

.

specifies that the cursor stays in the current cell when you press .

6. When done, press MATRIX to see the Matrix catalog, or press to return to HOME. The matrix entries are automatically stored.

Matrices 15-3


To transmit a matrix

A matrix is listed with two dimensions, even if it is 3×1. A vector is listed with the number of elements, such as 3.

You can send matrices between calculators just as you can send aplets, programs, lists, and notes.

1. Align the HP 39gs calculators’ infrared ports (or connect the calculators using an appropriate cable).

2. Open the Matrix catalogs on both calculators.

3. Highlight the matrix to send.

4. Press and choose the method of sending

(infrared or cable).

5. Press on the receiving calculator and choose the method of receiving (infrared or cable).

For more information on sending and receiving files, see


Working with matrices

To edit a matrix

Matrix edit keys

In the Matrix catalog, highlight the name of the matrix you want to edit and press .

The following table lists the matrix edit key operations.

Key Meaning

Copies the highlighted element to the edit line.

Inserts a row of zeros above, or a column of zeros to the left, of the highlighted cell. (You are prompted to choose row or column.)

A three-way toggle for cursor advancement in the Matrix editor.

advances to the right, advances downward, and

¸ does not advance at all.

Switches between larger and smaller font sizes.

15-4 Matrices


Key

CLEAR


Deletes the highlighted cells, row, or column (you are prompted to make a choice).

Clears all elements from the matrix.

Moves to the first row, last row, first column, or last column respectively.

To display a matrix

• In the Matrix catalog ( matrix name and press .

MATRIX ), highlight the

• In HOME, enter the name of the matrix variable and press .

To display one element

In HOME, enter matrixname(row,column). For example, if M2 is [[3,4],[5,6]], then M2(1,2)

4.

To create a matrix in HOME

1. Enter the matrix in the edit line. Start and end the matrix and each row with square brackets (the shifted

and keys).

2. Separate each element and each row with a comma.

Example: [[1,2],[3,4]].

3. Press to enter and display the matrix.

The left screen below shows the matrix

[[2.5,729],[16,2]] being stored into M5. The screen on the right shows the vector [66,33,11] being stored into M6. Note that you can enter an expression

(like 5/2) for an element of the matrix, and it will be evaluated.

Matrices 15-5


To store one element

In HOME, enter, value matrixname(row,column).

For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix:

728

M5 1 2

M5

.

An attempt to store an element to a row or column beyond the size of the matrix results in an error message.

Matrix arithmetic

You can use the arithmetic functions (+, –, ×, / and powers) with matrix arguments. Division left-multiplies by the inverse of the divisor. You can enter the matrices themselves or enter the names of stored matrix variables.

The matrices can be real or complex.

For the next examples, store [[1,2],[3,4]] into M1 and

[[5,6],[7,8]] into M2.

Example 1. Create the first matrix.

MATRIX

3 4

2. Create the second matrix.

MATRIX

5 6

7

8

15-6 Matrices


3. Add the matrices that you created.

M1

M2

To multiply and divide by a scalar

For division by a scalar, enter the matrix first, then the operator, then the scalar. For multiplication, the order of the operands does not matter.

The matrix and the scalar can be real or complex. For example, to divide the result of the previous example by

2, press the following keys:

2

To multiply two matrices

To raise a matrix to a power

To multiply the two matrices M1 and M2 that you created for the previous example, press the following keys:

M1 M

2

To multiply a matrix by a vector, enter the matrix first, then the vector. The number of elements in the vector must equal the number of columns in the matrix.

You can raise a matrix to any power as long as the power is an integer. The following example shows the result of raising matrix M1, created earlier, to the power of 5.

M1 5

Note: You can also raise a matrix to a power without first storing it as a variable.

Matrices can be raised to negative powers. In this case, the result is equivalent to 1/[matrix]^ABS(power). In the following example, M1 is raised to the power of –2.

Matrices 15-7


2

M1

To divide by a square matrix

For division of a matrix or a vector by a square matrix, the number of rows of the dividend (or the number of elements, if it is a vector) must equal the number of rows in the divisor.

This operation is not a mathematical division: it is a left- multiplication by the inverse of the divisor. M1/M2 is equivalent to M2

–1

* M1.

To divide the two matrices M1 and M2 that you created for the previous example, press the following keys:

M1

M2

To invert a matrix

You can invert a square matrix in HOME by typing the matrix (or its variable name) and pressing x

–1

. Or you can use the matrix INVERSE command.

Enter INVERSE(matrixname) in HOME and press

.

You can change the sign of each element in a matrix by pressing before the matrix name.

To negate each element

Solving systems of linear equations

Example Solve the following linear system:

+

+

4x y

+ x y z

+

–

– 2z

=

=

=

5

7

1

1. Open the Matrix catalog and create a vector.

MATRIX

15-8 Matrices


Matrices

2. Create the vector of the constants in the linear system.

1

3. Return to the Matrix

Catalog.

MATRIX

In this example, the vector you created is listed as M1.

4. Create a new matrix.

Select Real matrix

5. Enter the equation coefficients.

3 2

4

1 1

1 2

In this example, the matrix you created is listed as

M2.

6. Return to HOME and enter the calculation to left-multiply the constants vector by the inverse of the coefficients matrix.

M2

x

–1

M1

The result is a vector of the solutions x = 2, y = 3 and z = –2.

An alternative method, is to use the RREF function. See

“RREF” on page 15-12.

15-9


Matrix functions and commands

About functions

About commands

• Functions can be used in any aplet or in HOME. They are listed in the MATH menu under the Matrix category. They can be used in mathematical expressions—primarily in HOME—as well as in programs.

• Functions always produce and display a result. They do not change any stored variables, such as a matrix variable.

• Functions have arguments that are enclosed in parentheses and separated by commas; for example,

CROSS(vector1,vector2). The matrix input can be either a matrix variable name (such as M1) or the actual matrix data inside brackets. For example,

CROSS(M1,[1,2]).

Matrix commands are listed in the CMDS menu (

CMDS ), in the matrix category.

See “Matrix commands” on page 18-24 for details of the

matrix commands available for use in programming.

Functions differ from commands in that a function can be used in an expression. Commands cannot be used in an expression.

Argument conventions

• For row# or column#, supply the number of the row

(counting from the top, starting with 1) or the number of the column (counting from the left, starting with 1).

• The argument matrix can refer to either a vector or a matrix.

Matrix functions

COLNORM

Column Norm. Finds the maximum value (over all columns) of the sums of the absolute values of all elements in a column.

COLNORM(matrix)

15-10 Matrices


COND

CROSS

DET

DOT

EIGENVAL

EIGENVV

IDENMAT

INVERSE

LQ

LSQ

Matrices

Condition Number. Finds the 1-norm (column norm) of a square matrix.

COND(matrix)

Cross Product of vector1 with vector2.

CROSS(vector1, vector2)

Determinant of a square matrix.

DET(matrix)

Dot Product of two arrays, matrix1 matrix2.

DOT(matrix1, matrix2)

Displays the eigenvalues in vector form for matrix.

EIGENVAL(matrix)

Eigenvectors and Eigenvalues for a square matrix.

Displays a list of two arrays. The first contains the eigenvectors and the second contains the eigenvalues.

EIGENVV(matrix)

Identity matrix. Creates a square matrix of dimension

size × size whose diagonal elements are 1 and offdiagonal elements are zero.

IDENMAT(size)

Inverts a square matrix (real or complex).

INVERSE(matrix)

LQ Factorization. Factors an m × n matrix into three matrices:

{[[ m × n lowertrapezoidal]],[[ n × n orthogonal]],

[[ m × m permutation]]}.

LQ(matrix)

Least Squares. Displays the minimum norm least squares

matrix (or vector).

LSQ(matrix1, matrix2)

15-11


LU

MAKEMAT

QR

RANK

ROWNORM

RREF

SCHUR

SIZE

15-12

LU Decomposition. Factors a square matrix into three matrices:

{[[lowertriangular]],[[uppertriangular]],[[permutation]]}

The uppertriangular has ones on its diagonal.

LU(matrix)

Make Matrix. Creates a matrix of dimension rows ×

columns, using expression to calculate each element. If

expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J.

MAKEMAT(expression, rows, columns)

Example

MAKEMAT(0,3,3) returns a 3×3 zero matrix,

[[0,0,0],[0,0,0],[0,0,0]].

QR Factorization. Factors an m×n matrix into three matrices: {[[m×m orthogonal]],[[m×n

uppertrapezoidal]],[[n×n permutation]]}.

QR(matrix)

Rank of a rectangular matrix.

RANK(matrix)

Row Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row.

ROWNORM(matrix)

Reduced-Row Echelon Form. Changes a rectangular

matrix to its reduced row-echelon form.

RREF(matrix)

Schur Decomposition. Factors a square matrix into two matrices. If matrix is real, then the result is

{[[orthogonal]],[[upper-quasi triangular]]}.

If matrix is complex, then the result is

{[[unitary]],[[upper-triangular]]}.

SCHUR(matrix)

Dimensions of matrix. Returned as a list: {rows,columns}.

SIZE(matrix)

Matrices


SPECNORM

SPECRAD

SVD

SVL

TRACE

TRN

Spectral Norm of matrix.

SPECNORM(matrix)

Spectral Radius of a square matrix.

SPECRAD(matrix)

Singular Value Decomposition. Factors an m × n matrix into two matrices and a vector:

{[[m × m square orthogonal]],[[n × n square orthogonal]],

[real]}.

SVD(matrix)

Singular Values. Returns a vector containing the singular values of matrix.

SVL(matrix)

Finds the trace of a square matrix. The trace is equal to the sum of the diagonal elements. (It is also equal to the sum of the eigenvalues.)

TRACE(matrix)

Transposes matrix. For a complex matrix, TRN finds the conjugate transpose.

TRN(matrix)

Examples

Identity Matrix

You can create an identity matrix with the IDENMAT function. For example, IDENMAT(2) creates the 2×2 identity matrix [[1,0],[0,1]].

You can also create an identity matrix using the

MAKEMAT (make matrix) function. For example, entering

MAKEMAT(I¼J,4,4) creates a 4 × 4 matrix showing the numeral 1 for all elements except zeros on the diagonal.

The logical operator ¼ returns 0 when I (the row number) and J (the column number) are equal, and returns 1 when they are not equal.

Matrices 15-13


Transposing a

Matrix

Reduced-Row

Echelon Form

The TRN function swaps the row-column and column-row elements of a matrix. For instance, element 1,2 (row 1, column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on.

For example, TRN([[1,2],[3,4]]) creates the matrix

[[1,3],[2,4]].

The following set of equations –

2x y z

4x

+

–

+

2y

–

+

3z

=

2z

=

–

=

14

3

14 can be written as the augmented matrix

1 2 3 14

2 1 – 1 – 3

4 2 2 14 which can then stored as a

× real matrix in any matrix variable. M1 is used in this example.

You can use the RREF function to change this to reduced row echelon form, storing it in any matrix variable. M2 is used in this example.

The reduced row echelon matrix gives the solution to the linear equation in the fourth column.

An advantage of using the

RREF function is that it will also work with inconsistent matrices resulting from systems of equations which have no solution or infinite solutions.

For example, the following set of equations has an infinite number of solutions:

+

2x y

–

–

x 2y

–

+

= z

=

7

=

5

2

15-14 Matrices


The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions.

Matrices 15-15



16

Lists

Create a list in the List Catalog

You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matrices, all enclosed in braces.

A list may, for example, contain a sequence of real numbers such as {1,2,3}. (If the Decimal Mark mode is set to Comma, then the separators are periods.) Lists represent a convenient way to group related objects.

There are ten list variables available, named L0 to L9. You can use them in calculations or expressions in HOME or in a program. Retrieve the list names from the VARS menu, or just type their names from the keyboard.

You can create, edit, delete, send, and receive named lists in the List catalog ( LIST ). You can also create and store lists—named or unnnamed—in HOME lists

List variables are identical in behaviour to the columns

C1.C0 in the Statistics aplet. You can store a statistics column to a list (or vice versa) and use any of the list functions on the statistics columns, or the statistics functions, on the list variables.

1. Open the List catalog.

LIST .

2. Highlight the list name you want to assign to the new list (L1, etc.) and press to display the List editor.

Lists 16-1


List catalog keys

3. Enter the values you want in the list, pressing after each one.

Values can be real or complex numbers (or an expression). If you enter a calculation, it is evaluated and the result is inserted in the list.

4. When done, press or press

LIST to see the List catalog,

to return to HOME.

The list catalog keys are:

Key Meaning

Opens the highlighted list for editing.

Transmits the highlighted list to another hp 39gs or a PC. See

“Sending and receiving aplets” on page 19-4 for further information.

Receives a list from another

hp 39gs or a PC. See “Sending and receiving aplets” on page 19-4 for


CLEAR

Clears the highlighted list.

Clears all lists.

or Moves to the end or the beginning of the catalog.

16-2 Lists


List edit keys

When you press to create or change a list, the following keys are available to you:

Key

CLEAR

Meaning

Copies the highlighted list item into the edit line.

Inserts a new value before the highlighted item.

Deletes the highlighted item from the list.

Clears all elements from the list.

or Moves to the end or the beginning of the list.

Create a list in

HOME

1. Enter the list on the edit line. Start and end the list with braces (the shifted and keys) and separate each element with a comma.

2. Press to evaluate and display the list.

Immediately after typing in the list, you can store it in a variable by pressing listname list variable names are L0 through L9.

. The

This example stores the list {25,147,8} in L1.

Note: You can omit the final brace when entering a list.

Lists 16-3


Displaying and editing lists

To display a list

To display one element

To edit a list

• In the List catalog, highlight the list name and press

.

• In HOME, enter the name of the list and press

.

In HOME, enter listname(element#). For example, if L2 is

{3,4,5,6}, then L2(2) returns 4.


LIST .

2. Press or to highlight the name of the list you want to edit (L1, etc.) and press list contents.

to display the

16-4

3. Press or to highlight the element you want to edit. In this example, edit the third element so that it has a value of 5.

5

4. Press .

Lists


To insert an element in a list


LIST .

2. Press or to highlight the name of the list you want to edit

(L1, etc.) and press

to display the list contents.

New elements are inserted above the highlighted position. In this example, an element, with the value of 9, is inserted between the first and second elements in the list.

3. Press to the insertion position, then press

9.

, and press

4. Press .

To store one element

In HOME, enter value listname(element). For example, to store 148 as the second element in L1, type

148 L1(2) .

Lists 16-5


Deleting lists

To delete a list

In the List catalog, highlight the list name and press .

You are prompted to confirm that you want to delete the contents of the highlighted list variable. Press to delete the contents.

In the List catalog, press CLEAR .

To delete all lists

Transmitting lists

You can send lists to calculators or PCs just as you can aplets, programs, matrices, and notes.

1. Align the HP 39gs calculators’ infrared ports (or connect the calculators using an appropriate cable).

2. Open the List catalogs on both calculators.

3. Highlight the list to send.

4. Press and choose the method of sending

(infrared or cable).

5. Press on the receiving calculator and choose the method of receiving (infrared or cable).

For more information on sending and receiving files, see


List functions

List functions are found in the MATH menu. You can use them in HOME, as well as in programs.

You can type in the name of the function, or you can copy the name of the function from the List category of the MATH menu. Press (the alpha L character key). This highlights the List category in the left column. Press to move the cursor to the right column which contain the List functions, select a function, and press .

List functions have the following syntax:

• Functions have arguments that are enclosed in parentheses and separated by commas. Example:

16-6 Lists


CONCAT

Δ

LIST

CONCAT(L1,L2). An argument can be either a list variable name (such as L1) or the actual list. For example, REVERSE({1,2,3}).

• If Decimal Mark in Modes is set to Comma, use periods to separate arguments. For example,

CONCAT(L1.L2).

Common operators like +, –, ×, and / can take lists as arguments. If there are two arguments and both are lists, then the lists must have the same length, since the calculation pairs the elements. If there are two arguments and one is a real number, then the calculation pairs the number with each element of the list.

Example

5*{1,2,3} returns {5,10,15}.

Besides the common operators that can take numbers, matrices, or lists as arguments, there are commands that can only operate on lists.

Concatenates two lists into a new list.

CONCAT(list1,list2)

Example

CONCAT({1,2,3},{4}) returns {1,2,3,4}.

Creates a new list composed of the first differences, that is, the differences between the sequential elements in

list1. The new list has one fewer elements than list1. The first differences for {x

1

x

2

... x n

} are {x

2

–x

1

... x n

–x n–1

}.

ΔLIST(list1)

Lists 16-7


MAKELIST

ΠLIST

POS

16-8

Example

In HOME, store {3,5,8,12,17,23} in L5 and find the first differences for the list.

{3,5,8,12,17,23

}

L 5

L

Select Δ LIST

L5

Calculates a sequence of elements for a new list.

Evaluates expression with variable from begin to end values, taken at increment steps.

MAKELIST(expression,variable,begin,end, increment )

The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression.

Example

In HOME, generate a series of squares from 23 to 27.

L Select

MAKELIST

A

A 23

Calculates the product of all elements in list.

ΠLIST(list)

Example

ΠLIST({2,3,4}) returns 24.

Returns the position of an element within a list. The

element can be a value, a variable, or an expression. If there is more than one instance of the element, the

Lists


REVERSE

SIZE

ΣLIST

SORT

position of the first occurrence is returned. A value of 0 is returned if there is no occurrence of the specified element.

POS(list, element)

Example

POS ({3, 7, 12, 19},12) returns 3

Creates a list by reversing the order of the elements in a list.

REVERSE(list)

Calculates the number of elements in a list.

SIZE(list)

Also works with matrices.

Calculates the sum of all elements in list.

ΣLIST(list)

Example

ΣLIST({2,3,4}) returns 9.

Sorts elements in ascending order.

SORT(list)

Finding statistical values for list elements

To find values such as the mean, median, maximum, and minimum values of the elements in a list, use the Statistics aplet.

Example

In this example, use the Statistics aplet to find the mean, median, maximum, and minimum values of the elements in the list, L1.

1. Create L1 with values 88, 90, 89, 65, 70, and 89.

{ 88 90

}

L1

Lists 16-9


16-10

2. In HOME, store L1 into

C1. You will then be able to see the list data in the Numeric view of the

Statistics aplet.

L1

C1

3. Start the Statistics aplet, and select 1-variable mode

(press , if necessary, to display ).

Select

Statistics

Note: Your list values are now in column 1 (C1).

4. In the Symbolic view, define H1 (for example) as C1

(sample) and 1 (frequency).

5. Go to the Numeric view to display calculated statistics.

See “One-variable” on page 10-14 for the meaning

of each computed statistic.

Lists


17

Notes and sketches

Introduction

The HP 39gs has text and picture editors for entering notes and sketches.

• Each aplet has its own independent Note view and

Sketch view. Notes and sketches that you create in these views are associated with the aplet. When you save the aplet, or send it to another calculator, the notes and sketches are saved or sent as well.

• The Notepad is a collection of notes independent of all aplets. These notes can also be sent to another calculator via the Notepad Catalog.

Aplet note view

You can attach text to an aplet in its Note view.

To write a note in

Note view

1. In an aplet, press NOTE for the Note view.

2. Use the note editing keys shown in the table in the following section.

3. Set Alpha lock ( ) for quick entry of letters. For

lowercase Alpha lock, press .

4. While Alpha lock is on:

– To type a single letter of the opposite case, press

letter.

– To type a single non-alpha character (such as 5 or [ ), press first. (This turns off Alpha lock for one character.)

Your work is automatically saved. Press any view key

( , the Notes view.

, , ) or to exit

Notes and sketches 17-1


Note edit keys

Key

CLEAR

CMDS

CHARS

Meaning

Space key for text entry.

Displays next page of a multi-page note.

Alpha-lock for letter entry.

Lower-case alpha-lock for letter entry.

Backspaces cursor and deletes character.

Deletes current character.

Starts a new line.

Erases the entire note.

Menu for entering variable names, and contents of variables.

Menu for entering math operations, and constants.

Menu for entering program commands.

Displays special characters. To type one, highlight it and press

. To copy a character without closing the CHARS screen, press

.

17-2 Notes and sketches

Aplet sketch view

(

You can attach pictures to an aplet in its Sketch view

SKETCH ). Your work is automatically saved with the aplet. Press any other view key or

Sketch view

to exit the

Sketch keys

Key

CLEAR

Meaning

Stores the specified portion of the current sketch to a graphics variable (G1 through G0).

Adds a new, blank page to the current sketch set.

Displays next sketch in the sketch set. Animates if held down.

Opens the edit line to type a text label.

Displays the menu-key labels for drawing.

Deletes the current sketch.

Erases the entire sketch set.

Toggles menu key labels on and off. If menu key labels are hidden,

or any menu key, redisplays the menu key labels.

To draw a line

1. In an aplet, press SKETCH for the Sketch view.

2. In Sketch view, press and move the cursor to where you want to start the line

3. Press . This turns on line-drawing.

4. Move the cursor in any direction to the end point of the line by pressing the , , , keys.

5. Press to finish the line.



To draw a box

To draw a circle

DRAW keys

1. In Sketch view, press and move the cursor to where you want any corner of the box to be.

2. Press .

3. Move the cursor to mark the opposite corner for the box. You can adjust the size of the box by moving the cursor.

4. Press to finish the box.

1. In Sketch view, press and move the cursor to where you want the center of the circle to be.

2. Press . This turns on circle drawing.

3. Move the cursor the distance of the radius.

4. Press to draw the circle.

Key Meaning

Dot on. Turns pixels on as the cursor moves.

Dot off. Turns pixels off as the cursor moves.

Draws a line from the cursor’s starting position to the cursor’s current position.

Press when you have finished. You can draw a line at any angle.

Draws a box from the cursor’s starting position to the cursor’s current position.

Press when you have finished.

Draws a circle with the cursor’s starting position as the center. The radius is the distance between the cursor’s starting and ending position. Press to draw the circle.



To label parts of a sketch

1. Press and type the text on the edit line. To lock the Alpha shift on, press (for uppercase) or

To make the label a smaller character size, turn off

before pressing . ( is a toggle between small and large font size). The smaller character size cannot display lowercase letters.

2. Press .

3. Position the label where you want it by pressing the

To create a set of sketches

To store into a graphics variable

4. Press again to affix the label.

5. Press to continue drawing, or press

to exit the

Sketch view.

You can create a set of up to ten sketches. This allows for simple animation.

• After making a sketch, press to add a new, blank page. You can now make a new sketch, which becomes part of the current set of sketches.

• To view the next sketch in an existing set, press

. Hold down for animation.

• To remove the current page in the current sketch series, press .

You can define a portion of a sketch inside a box, and then store that graphic into a graphics variable.

1. In the Sketch view, display the sketch you want to copy (store into a variable).

2. Press .

3. Highlight the variable name you want to use and press .

4. Draw a box around the portion you want to copy: move the cursor to one corner, press , then move the cursor to the opposite corner, and press .



To import a graphics variable

You can copy the contents of a graphics variable into the

Sketch view of an aplet.

1. Open the Sketch view of the aplet (

The graphic will be copied here.

2. Press , .

SKETCH ).

3. Highlight Graphic, then press and highlight the name of the variable ( G1, etc.).

4. Press variable.

to recall the contents of the graphics

5. Move the box to where you would like to copy the graphic, then press .

The notepad

To create a note in the Notepad

Subject to available memory, you can store as many notes as you want in the Notepad ( NOTEPAD ).

These notes are independent of any aplet. The Notepad catalog lists the existing entries by name. It does not

include notes that were created in aplets’ Note views, but

these can be imported. See “To import a note” on

page 17-8.

1. Display the Notepad catalog.

NOTEPAD

2. Create a new note.

3. Enter a name for your note.

MYNOTE



Notepad Catalog keys

4. Write your note.

See “Note edit keys” on page 17-2 for more

information on the entry and editing of notes.

5. When you are finished, press or an aplet key to exit Notepad. Your work is automatically saved.

Key

CLEAR

Meaning

Opens the selected note for editing.

Begins a new note, and asks for a name.

Transmits the selected note to another HP 39gs or PC.

Receives a note being transmitted from another HP

39gs or PC.

Deletes the selected note.

Deletes all notes in the catalog.



To import a note

You can import a note from the Notepad into an aplet’s

Note view, and vice versa. Suppose you want to copy a note named “Assignments” from the Notepad into the

Function Note view:

1. In the Function aplet, display the Note view

( NOTE ).

column, then highlight the name “Assignments” in the right column.

3. Press to copy the contents of

“Assignments” to the Function Note view.

Note: To recall the name instead of the contents,

press instead of .

Suppose you want to copy the Note view from the current aplet into the note, Assignments, in the Notepad.

1. In the Notepad (

“Assignments”.

NOTEPAD ), open the note, column, then press and highlight NoteText in the right column.

3. Press to recall the contents of the Note view into the note “Assignments”.



18

Programming

Introduction

H I N T

The Contents of a

Program

Structured

Programming

This chapter describes how to program using the hp

39gs. In this chapter you’ll learn about:

• using the Program catalog to create and edit programs

• programming commands

• storing and retrieving variables in programs

• programming variables.

More information on programming, including examples and special tools, can be found at HP’s calculators web site: http://www.hp.com/calculators

An HP 39gs program contains a sequence of numbers, mathematical expressions, and commands that execute automatically to perform a task.

These items are separated by a colon ( : ). Commands that take multiple arguments have those arguments separated by a semicolon ( ; ). For example,

PIXON xposition;yposition:

Inside a program you can use branching structures to control the execution flow. You can take advantage of structured programming by creating building-block programs. Each building-block program stands alone—and it can be called from other programs. Note:

If a program has a space in its name then you have to put

quotes around it when you want to run it.

Programming 18-1


Example RUN GETVALUE: RUN CALCULATE: RUN

"SHOW ANSWER":

This program is separated into three main tasks, each an individual program. Within each program, the task can be simple—or it can be divided further into other programs that perform smaller tasks.

Program catalog

The Program catalog is where you create, edit, delete, send, receive, or run programs. This section describes how to

• open the Program catalog

• create a new program

• enter commands from the program commands menu

• enter functions from the MATH menu

• edit a program

• run and debug a program

• stop a program

• copy a program

• send and receive a program

• delete a program or its contents

• customize an aplet.

Open Program

Catalog

18-2

1. Press PROGRM .

The Program Catalog displays a list of program names. The Program Catalog contains a built-in entry called Editline.

Editline contains the last expression that you entered from the edit line in HOME, or the last data you entered in an input form. (If you press from HOME without entering any data, the HP 39gs runs the contents of Editline.)

Before starting to work with programs, you should take a few minutes to become familiar with the

Program catalog menu keys. You can use any of the following keys (both menu and keyboard), to perform tasks in the Program catalog.

Programming


Program catalog keys

The program catalog keys are:

Key

or

CLEAR

Meaning

Opens the highlighted program for editing.

Prompts for a new program name, then opens an empty program.

Transmits the highlighted program to another HP 39gs or to a disk drive.

Receives the highlighted program from another HP 39gs or from a disk drive.

Runs the highlighted program.

Moves to the beginning or end of the Program catalog.

Deletes the highlighted program.

Deletes all programs in the program catalog.

Programming 18-3


Creating and editing programs

Create a new program

1. Press PROGRM to open the Program catalog.

2. Press .

The HP 39gs prompts you for a name.

A program name can contain special characters, such as a space. However, if you use special characters and then run the program by typing it in

HOME, you must enclose the program name in double quotes (" "). Don't use the " symbol within your program name.

3. Type your program name, then press .

When you press , the Program Editor opens.

4. Enter your program. When done, start any other activity. Your work is saved automatically.

Enter commands

Until you become familiar with the HP 39gs commands, the easiest way to enter commands is to select them from the Commands menu from the Program editor. You can also type in commands using alpha characters.

CMDS to open 1. From the Program editor, press the Program Commands menu.

CMDS

18-4 Programming


2. On the left, use or to highlight a command category, then press to access the commands in the category. Select the command that you want.

3. Press to paste the command into the program editor.

Edit a program


2. Use the arrow keys to highlight the program you want to edit, and press . The HP 39gs opens the

Program Editor. The name of your program appears in the title bar of the display. You can use the following keys to edit your program.

Programming 18-5


Editing keys

The editing keys are:

Key

CLEAR

CMDS

CHARS

Meaning

Inserts the editing point.

character at the

Inserts space into text.

Displays previous page of the program.

Displays next page of the program.

Moves up or down one line.

Moves right or left one character.

Alpha-lock for letter entry. Press

A...Z to lock lower case.

Backspaces cursor and deletes character.

Deletes current character.

Starts a new line.

Erases the entire program.

Displays menus for selecting variable names, contents of variables, math functions, and program constants.

Displays menus for selecting program conmmands.

Displays all characters. To type one, highlight it and press .

To enter several characters in a row, use the

CHARS menu.

menu key while in the

18-6 Programming


Using programs

Run a program

From HOME, type RUN program_name. or

From the Program catalog, highlight the program you want to run and press

Regardless of where you start the program, all programs

run in HOME. What you see will differ slightly depending on where you started the program. If you start the program from HOME, the HP 39gs displays the contents of Ans (Home variable containing the last result), when the program has finished. If you start the program from the Program catalog, the hp39gs returns you to the

Program catalog when the program ends.

Debug a program

If you run a program that contains errors, the program will stop and you will see an error message.

To debug the program:

1. Press to edit the program.

The insert cursor appears in the program at the point where the error occurred.

2. Edit the program to fix the error.

3. Run the program.

4. Repeat the process until you correct all errors.

Stop a program

You can stop the running of a program at any time by pressing CANCEL

(the Note: You may have to press it a couple of times.

Programming 18-7


Copy a program

You can use the following procedure if you want to make a copy of your work before editing—or if you want to use one program as a template for another.

1. Press

2. Press .

PROGRM to open the Program catalog.

3. Type a new file name, then choose .

The Program Editor opens with a new program.

4. Press to open the variables menu.

5. Press to quickly scroll to Program.

6. Press , then highlight the program you want to copy.

Transmit a program

H I N T

The contents of the highlighted program are copied into the current program at the cursor location.

If you use a programming routine often, save the routine under a different program name, then use the above method to copy it into your programs.

You can send programs to, and receive programs from, other calculators just as you can send and receive aplets, matrices, lists, and notes.

After aligning the calculators’ infrared ports, open the

Program catalogs on both calculators. Highlight the program to send, then press on the sending calculator and on the receiving calculator.

You can also send programs to, and receive programs from, a remote storage device (aplet disk drive or computer). This takes place via a cable connection and requires an aplet disk drive or specialized software running on a PC (such as a connectivity kit).

18-8 Programming


Delete a program

To delete a program:


2. Highlight a program to delete, then press .

Delete all programs

Delete the contents of a program

You can delete all programs at once.

1. In the Program catalog, press

2. Press .

CLEAR .

You can clear the contents of a program without deleting the program name.


2. Highlight a program, then press .

3. Press CLEAR , then press .

4. The contents of the program are deleted, but the program name remains.

Customizing an aplet

You can customize an aplet and develop a set of programs to work with the aplet.

Use the SETVIEWS command to create a custom VIEWS menu which links specially written programs to the new aplet.

A useful method for customizing an aplet is illustrated below:

1. Decide on the built-in aplet that you want to customize. For example you could customize the

Function aplet or the Statistics aplet. The customized aplet inherits all the properties of the built-in aplet.

Save the customized aplet with a unique name.

2. Customize the new aplet if you need to, for example by presetting axes or angle measures.

3. Develop the programs to work with your customized aplet. When you develop the aplet’s programs, use the standard aplet naming convention. This allows you to keep track of the programs in the Program

catalog that belong to each aplet. See “Aplet naming convention” on page 18-10.

Programming 18-9


Aplet naming convention

To assist users in keeping track of aplets and associated programs, use the following naming convention when setting up an aplet’s programs:

• Start all program names with an abbreviation of the aplet name. We will use APL in this example.

• Name programs called by menu entries in the VIEWS menu number, after the entry, for example:

– APL.ME1 for the program called by menu option

1

– APL.ME2 for the program called by menu option

2

• Name the program that configures the new VIEWS menu option APL.SV where SV stands for SETVIEWS.

For example, a customized aplet called “Differentiation” might call programs called DIFF.ME1, DIFF.ME2, and

DIFF.SV.

Example

4. Develop a program that uses the SETVIEWS command to modify the aplet’s VIEWS menu. The menu options provide links to associated programs.

You can specify any other programs that you want

transferred with the aplet. See “SETVIEWS” on page

18-14 for information on the command.

5. Ensure that the customized aplet is selected, then run the menu configuration program to configure the aplet’s VIEWS menu.

6. Test the customized aplet and debug the associated programs. (Refer to “Debug a program” on page

16-7).

This example aplet is designed to demonstrate the process of customizing an aplet. The new aplet is based on the Function aplet. Note: This aplet is not intended to serve a serious use, merely to illustrate the process.

18-10 Programming


Save the aplet

1. Open the Function aplet and save it as

“EXPERIMENT”. The new aplet appears in the Aplet library.

Select

Function

EXPERIMENT

2. Create a program called EXP.ME1 with contents as shown. This program configures the plot ranges, then runs a program that allows you to set the angle format.

3. Create a program called EXP.ME2 with contents as shown. This program sets the numeric view options for the aplet, and runs the program that you can use to configure the angle mode.

4. Create a program called EXP.ANG which the previous two programs call.

Configuring the

Setviews menu option programs

5. Create a program called EXP.S which runs when you start the aplet, as shown. This program sets the angle mode to degrees, and sets up the initial function that the aplet plots.

In this section we will begin by configuring the

VIEWS menu by using the SETVIEWS command. We will then create the “helper” programs called by the

VIEWS menu which will do the actual work.

Programming 18-11


6. Open the Program catalog and create a program named “EXP.SV”. Include the following code in the program.

Each entry line after the command SETVIEWS is a trio that consists of a VIEWS menu text line (a space indicates none), a program name, and a number that defines the view to go to after the program has run its course. All programs listed here will transfer with an aplet when the aplet is transferred.

SETVIEWS ’’ ’’; ’’ ’’; 18;

Sets the first menu option to be “Auto scale”. This is the fourth standard Function aplet view menu option and the 18 “Auto scale”, specifies that it is to be included in the new menu. The empty quotes will ensure that the old name of “Auto scale” appears on the new menu. See

“SETVIEWS” on page 18-14.

’’ My Entry1’’;’’EXP.ME1’’;1;

Sets the second menu option. This option runs program EXP.ME1, then returns to view 1, Plot view.

’’ My Entry2’’;’’EXP.ME2’’;3;

Sets the third menu option. This option runs the program EXP.ME2, then returns to view 3, the NUM view.

’’ ’’;’’ EXP.SV’’;0;

This line specifies that the program to set the View menu (this program) is transferred with the aplet. The space character between the first set of quotes in the trio specifies that no menu option appears for the entry. You do not need to transfer this program with the aplet, but it allows users to modify the aplet’s menu if they want to.

18-12 Programming


’’ ’’;’’ EXP.ANG’’;0;

The program EXP.ANG is a small routine that is called by other programs that the aplet uses. This entry specifies that the program EXP.ANG is transferred when the aplet is transferred, but the space in the first quotes ensures that no entry appears on the menu.

’’Start’’;’’EXP.S’’;7:

This specifies the Start menu option. The program that is associated with this entry,

EXP.S, runs automatically when you start the aplet. Because this menu option specifies view 7, the VIEWS menu opens when you start the aplet.

You only need to run this program once to configure your aplet’s VIEWS menu. Once the aplet’s VIEWS menu is configured, it remains that way until you run

SETVIEWS again.

You do not need to include this program for your aplet to work, but it is useful to specify that the program is attached to the aplet, and transmitted when the aplet is transmitted.

7. Return to the program catalog. The programs that you created should appear as follows:

8. You must now the program EXP.SV to execute the SETVIEWS command and create the modified VIEWS menu. Check that the name of the new aplet is highlighted in the Aplet view.

9. You can now return to the Aplet library and press

to run your new aplet.

Programming commands

This section describes the commands for programming with hp 39GS. You can enter these commands in your program by typing them or by accessing them from the

Commands menu.

Programming 18-13


Aplet commands

CHECK

SELECT

SETVIEWS

18-14

Checks (selects) the corresponding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. Then a checkmark would appear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view.

CHECK n:

Selects the named aplet and makes it the current aplet.

Note: Quotes are needed if the name contains spaces or other special characters.

SELECT apletname:

The SETVIEWS command is used to define entries in the

VIEWS menu for aplets that you customize. See

“Customizing an aplet” on page 18-9 for an example of

using the SETVIEWS command.

When you use the SETVIEWS command, the aplet’s standard VIEWS menu is deleted and the customized menu is used in its place. You only need to apply the command to an aplet once. The VIEWS menu changes remain unless you apply the command again.

Typically, you develop a program that uses the

SETVIEWS command only. The command contains a trio of arguments for each menu option to create, or program to attach. Keep the following points in mind when using this command:

• The SETVIEWS command deletes an aplet’s standard

Views menu options. If you want to use any of the standard options on your reconfigured VIEWS menu, you must include them in the configuration.

• When you invoke the SETVIEWS command, the changes to an aplet’s VIEWS menu remain with the aplet. You need to invoke the command on the aplet again to change the VIEWS menu.

• All the programs that are called from the VIEWS menu are transferred when the aplet is transferred, for example to another calculator or to a PC.

• As part of the VIEWS menu configuration, you can specify programs that you want transferred with the aplet, but are not called as menu options. For example, these can be sub-programs that menu

Programming


Programming options use, or the program that defines the aplet’s

VIEWS menu.

• You can include a “Start” option in the VIEWS menu to specify a program that you want to run automatically when the aplet starts. This program typically sets up the aplet’s initial configuration. The

START option on the menu is also useful for resetting the aplet.

Command syntax

The syntax for the command is as follows:

SETVIEWS

"Prompt1" ;"ProgramName1";ViewNumber1;

"Prompt2" ;"ProgramName2";ViewNumber2:

(You can repeat as many Prompt/ProgramName/

ViewNumber trios of arguments as you like.)

Within each Prompt/ProgramName/ViewNumber trio, you separate each item with a semi-colon.

Prompt

Prompt is the text that is displayed for the corresponding entry in the Views menu. Enclose the prompt text in double quotes.

Associating programs with your aplet

If Prompt consists of a single space, then no entry appears in the view menu. The program specified in the

ProgramName item is associated with the aplet and transferred whenever the aplet is transmitted. Typically, you do this if you want to transfer the Setviews program with the aplet, or you want to transfer a sub-program that other menu programs use.

Auto-run programs

If the Prompt item is “Start”, then the ProgramName program runs whenever you start the aplet. This is useful for setting up a program to configure the aplet. Users can select the Start item from the VIEWS menu to reset the aplet if they change configurations.

You can also define a menu item called “Reset” which is auto-run if the user chooses the button in the APLET view.

18-15


ProgramName

ProgramName is the name of the program that runs when the corresponding menu entry is selected. All programs that are identified in the aplet’s SETVIEWS command are transferred when the aplet is transmitted.

ViewNumber

ViewNumber is the number of a view to start after the program finishes running. For example, if you want the menu option to display the Plot view when the associated program finishes, you would specify 1 as the

ViewNumber value.

Including standard menu options

To include one of an aplet’s standard VIEWS menu options in your customized menu, set up the arguments trio as follows:

• The first argument specifies the menu item name:

– Leave the argument empty to use the standard

Views menu name for the item, or

– Enter a menu item name to replace the standard name.

• The second argument specifies the program to run:

– Leave the argument empty to run the standard menu option.

– Insert a program name to run the program before the standard menu option is executed.

• The third argument specifies the view and the menu number for the item. Determine the menu number from the View numbers table below.

Note: SETVIEWS with no arguments resets the views to default of the base aplet.

18-16 Programming


UNCHECK

View numbers

The Function aplet views are numbered as follows:

5

6

3

4

0

1

2

7

8

9

10

HOME

Plot

Symbolic

Numeric

Plot-Setup

Symbolic-Setup

Numeric-Setup

Views

Note

Sketch view

Aplet Catalog

14

15

16

17

11

12

13

18

19

20

21

List Catalog

Matrix Catalog

Notepad Catalog

Program Catalog

Plot-Detail

Plot-Table

Overlay Plot

Auto scale

Decimal

Integer

Trig

View numbers from 15 on will vary according to the parent aplet. The list shown above is for the Function aplet. Whatever the normal VIEWS menu for the parent aplet, the first entry will become number 15, the second number 16 and so on.

Unchecks (unselects) the corresponding function in the current aplet. For example, Uncheck 3 would uncheck F3 if the current aplet is Function.

UNCHECK n:

Branch commands

Branch commands let a program make a decision based on the result of one or more tests. Unlike the other programming commands, the branch commands work in logical groups. Therefore, the commands are described together rather than each independently.

IF...THEN...END

Executes a sequence of commands in the true-clause only if the test-clause evaluates to true. Its syntax is:

IF test-clause

THEN true-clause END

Programming 18-17


IF... THEN... ELSE...

END

CASE...END

IFERR...

THEN...

ELSE…

END...

Example

1 A :

IF A==1

THEN MSGBOX " A EQUALS 1" :

END:

Executes the true-clause sequence of commands if the test-

clause is true, or the false-clause sequence of commands if the test-clause is false.

IF test-clause

THEN true-clause ELSE false-clause END

Example

1 A :

IF A==1 THEN

MSGBOX "A EQUALS 1" :

ELSE

MSGBOX "A IS NOT EQUAL TO 1" :

END:

Executes a series of test-clause commands that execute the appropriate true-clause sequence of commands. Its syntax is:

.

.

CASE

IF test-clause

1

THEN true-clause

1

END

IF test-clause

2

THEN true-clause

2

END

.

IF test-clause n

THEN true-clause n

END

END:

When CASE is executed, test-clause

1 test is true, true-clause

1 to END. If test-clause

1 clause

2

is evaluated. If the

is executed, and execution skips

if false, execution proceeds to test-

. Execution with the CASE structure continues until a true-clause is executed (or until all the test-clauses evaluate to false).

Many conditions are automatically recognized by the HP

39gs as error conditions and are automatically treated as errors in programs.

18-18 Programming


RUN

STOP

IFERR...THEN...ELSE…END allows a program to intercept error conditions that otherwise would cause the program to abort. Its syntax is:

IFERR trap-clause

THEN clause_1

ELSE clause_2

END :

Example

IFERR

60/X Y:

THEN

MSGBOX "Error: X is zero.":

ELSE

MSGBOX "Value is "Y:

END:

Runs the named program. If your program name contains special characters, such as a space, then you must enclose the file name in double quotes (" ").

RUN "program name": or RUN programname:

Stops the current program.

STOP:

Drawing commands

The drawing commands act on the display. The scale of the display depends on the current aplet's Xmin, Xmax,

Ymin, and Ymax values. The following examples assume the hp 39gs default settings with the Function aplet as the current aplet.

ARC

Draws a circular arc, of given radius, whose centre is at

(x,y) The arc is drawn from start_angle_measurement, to

end_angle_measurement.

ARC x;y;radius;start_angle_measurement ;

end_angle_measurement:

Programming 18-19

ERASE

FREEZE

LINE

PIXOFF

PIXON

TLINE


BOX

18-20

Example

ARC 0;0;2;0;2π:

FREEZE:

Draws a circle centered at (0,0) of radius 2. The

FREEZE command causes the circle to remain displayed on the screen until you press a key.

Draws a box with diagonally opposite corners (x1,y1) and

(x2,y2).

BOX x1;y1;x2;y2:

Example

BOX -1;-1;1;1:

FREEZE:

Draws a box, lower corner at (–1,–1), upper corner at (1,1)

Clears the display

ERASE:

Halts the program, freezing the current display.

Execution resumes when any key is pressed.

Draws a line from (x1, y1) to (x2, y2).

LINE x1;y1;x2;y2:

Turns off the pixel at the specified coordinates (x,y).

PIXOFF x;y:

Turns on the pixel at the specified coordinates (x,y).

PIXON x;y:

Toggles the pixels along the line from (x1, y1) to (x2, y2) on and off. Any pixel that was turned off, is turned on; any pixel that was turned on, is turned off. TLINE can be used to erase a line.

TLINE x1;y1;x2;y2:

Programming


Example

TLINE 0;0;3;3:

Erases previously drawn 45 degree line from (0,0) to

(3,3), or draws that line if it doesn’t already exist.

Graphic commands

The graphic commands use the graphics variables G0 through G9—or the Page variable from Sketch—as

graphicname arguments. The position argument takes the form ( x,y). Position coordinates depend on the current aplet’s scale, which is specified by Xmin, Xmax, Ymin, and Ymax. The upper left corner of the target graphic

(graphic2) is at (Xmin,Ymax).

You can capture the current display and store it in G0 by simultaneously pressing + .

DISPLAY→

→

DISPLAY

Stores the current display in graphicname.

DISPLAY→ graphicname:

Displays graphic from graphicname in the display.

→DISPLAY graphicname:

→GROB

Creates a graphic from expression, using font_size, and stores the resulting graphic in graphicname. Font sizes are 1, 2, or 3. If the fontsize argument is 0, the HP 39gs creates a graphic display like that created by the SHOW operation.

→GROB graphicname;expression; fontsize:

GROBNOT

Replaces graphic in graphicname with bitwise-inverted graphic.

GROBNOT graphicname:

GROBOR

Using the logical OR, superimposes graphicname2 onto

graphicname1. The upper left corner of graphicname2 is placed at position.

GROBOR graphicname1;(position);graphicname2:

Example

GROBOR G0; (1,1); G1:

Programming 18-21


GROBXOR

MAKEGROB

PLOT→

→PLOT

REPLACE

SUB

18-22 will superimpose G1 onto G0 starting a position (1,1), where the position is given in terms of the current axes settings, not as a pixel position.

Using the logical XOR, superimposes graphicname2 onto

graphicname1. The upper left corner of graphicname2 is placed at position.

GROBXOR graphicname1 ;(position) ;graphicname2:

Creates graphic with given width, height, and hexadecimal data, and stores it in graphicname.

MAKEGROB graphicname;width;height;hexdata:

Stores the Plot view display as a graphic in graphicname.

PLOT→ graphicname:

PLOT→ and DISPLAY→ can be used to transfer a copy of the current PLOT view into the sketch view of the aplet for later use and editing.

Example

1 PageNum:

PLOT→ Page:

→ DISPLAY Page:

FREEZE:

This program stores the current PLOT view to the first page in the sketch view of the current aplet and then displays the sketch as a graphic object until any key is pressed.

Puts graph from graphicname into the Plot view display.

→PLOT graphicname:

Replaces portion of graphic in graphicname1 with graphicname2 , starting at position. REPLACE also works for lists and matrices.

REPLACE graphicname1 ;(position);graphicname2:

Extracts a portion of the named graphic (or list or matrix), and stores it in a new variable, name. The portion is specified by position and positions.

SUB name;graphicname;(position);(positions):

Programming


ZEROGROB

Creates a blank graphic with given width and height, and stores it in graphicname.

ZEROGROB graphicname;width;height:

Loop commands

Loop hp allow a program to execute a routine repeatedly.

The HP 39gs has three loop structures. The example programs below illustrate each of these structures incrementing the variable A from 1 to 12.

DO…UNTIL …END

Do ... Until ... End is a loop command that executes the

loop-clause repeatedly until test-clause returns a true

(nonzero) result. Because the test is executed after the loop-clause, the loop-clause is always executed at least once. Its syntax is:

WHILE…

REPEAT…

END

FOR…TO…STEP

...END

Programming

DO loop-clause UNTIL test-clause END

1 A:

DO

A + 1 A

DISP 3;A:

UNTIL A == 12 END:

While ... Repeat ... End is a loop command that repeatedly evaluates test-clause and executes loop-clause sequence if the test is true. Because the test-clause is executed before the loop-clause, the loop-clause is not executed if the test is initially false. Its syntax is:

WHILE test-clause REPEAT loop-clause END

1 A:

WHILE A < 12 REPEAT

A+1 A

DISP 3;A:

END:

FOR name=start-expression TO end-expression

[STEP increment]; loop-clause END

FOR A=1 TO 12 STEP 1;

DISP 3;A:

END:

18-23


BREAK

Terminates loop.

BREAK:

Matrix commands

The matrix commands take variables M0–M9 as arguments.

ADDCOL

Note that the STEP parameter is optional. If it is omitted, a step value of 1 is assumed.

Add Column. Inserts values into a column before

column_number in the specified matrix. You enter the

values as a vector. The values must be separated by commas and the number of values must be the same as the number of rows in the matrix name.

ADDCOL name ;[value

1

,...,value n

];column_number:

ADDROW

Add Row. Inserts values into a row before row_number in the specified matrix. You enter the values as a vector. The values must be separated by commas and the number of values must be the same as the number of columns in the matrix name.

ADDROW name;[value

1

,..., value n

];row_number:

DELCOL

Delete Column. Deletes the specified column from the specified matrix.

DELCOL name;column_number:

DELROW

Delete Row. Deletes the specified row from the specified matrix.

DELROW name;row_number:

EDITMAT

Starts the Matrix Editor and displays the specified matrix.

If used in programming, returns to the program when user presses .

EDITMAT name:

18-24 Programming


RANDMAT

REDIM

REPLACE

SCALE

SCALEADD

SUB

SWAPCOL

SWAPROW

Programming

Creates random matrix with a specified number of rows and columns and stores the result in name

(name must be M0...M9). The entries will be integers ranging from –9 to 9.

RANDMAT name;rows;columns:

Redimensions the specified matrix or vector to size. For a matrix, size is a list of two integers {n1,n2}. For a vector,

size is a list containing one integer {n}.

REDIM name;size:

Replaces portion of a matrix or vector stored in name with an object starting at position start . start for a matrix is a list containing two numbers; for a vector, it is a single number. Replace also works with lists and graphics.

REPLACE name;start;object:

Multiplies the specified row_number of the specified matrix by value.

SCALE name;value;rownumber:

Multiplies the row of the matrix name by value, then adds this result to the second specified row.

SCALEADD name;value;row1;row2:

Extracts a sub-object—a portion of a list, matrix, or graphic from object—and stores it into name. start and

end are each specified using a list with two numbers for a matrix, a number for vector or lists, or an ordered pair,

( X,Y), for graphics.

SUB name;object;start;end:

Swaps Columns. Exchanges column1 and column2 of the specified matrix.

SWAPCOL name;column1;column2:

Swap Rows. Exchanges row1 and row2 in the specified matrix.

SWAPROW name;row1;row2:

18-25


Print commands

These commands print to an HP infrared printer, for example the HP 82240B printer.

PRDISPLAY

Prints the contents of the display.

PRDISPLAY:

PRHISTORY

Prints all objects in the history.

PRHISTORY:

PRVAR

Prints name and contents of variablename.

PRVAR variablename:

You can also use the PRVAR command to print the contents of a program or a note.

PRVAR programname;PROG:

PRVAR notename;NOTE:

Prompt commands

BEEP

CHOOSE

Beeps at the frequency and for the time you specify.

BEEP frequency;seconds:

Creates a choose box, which is a box containing a list of options from which the user chooses one. Each option is numbered, 1 through n. The result of the choose command is to store the number of the option chosen in a variable. The syntax is

CHOOSE variable_name; title; option

1

; option

2

;

...option n

: where variable_name is the number of the option that will be highlighted by default whenever the choose box is displayed, title is the text displayed in the title bar of the choose box, and option

1 in the choose box.

...option

n

are the options listed

18-26 Programming


CLRVAR

DISP

DISPXY

Programming

Example

3 A:CHOOSE A;

"COMIC STRIPS";

"DILBERT";

"CALVIN&HOBBES";

"BLONDIE":

Clears the specified variable. The syntax is:

CLRVAR variable :

Example

If you have stored

{1,2,3,4} in variable L1, entering CLVAR L1 will clear L1.

Displays textitem in a row of the display at the

line_number. A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings. Lines are numbered from the top of the screen, 1 being the top and 7 being the bottom.

DISP line_number;textitem:

Example

DISP 3;"A is" 2+2

Result: A is 4

(displayed on line 3)

Displays object at position (x_pos, y_pos) in size font. The syntax is:

DISPXY x_pos;y_pos;font;object:

The value of object can be a text string, a variable, or a combination of both. x_pos and y_pos are relative to the current settings of Xmin, Xmax, Ymin and Ymax (which you set in the PLOT SETUP view). The value of font is either

1 (small) or 2 (large).

18-27


DISPTIME

EDITMAT

FREEZE

Example

DISPXY

–3.5;1.5;2;"HELLO

WORLD":

Displays the current date and time.

DISPTIME

To set the date and time, simply store the correct settings in the date and time variables. Use the following formats:

M.DDYYYY for the date and H.MMSS for the time.

Examples

5.152000 DATE(sets the date to May 15, 2000).

10.1500 TIME (sets the time to 10:15 am).

Matrix Editor. Opens the Matrix editor for the specified matrix. Returns to the program when user presses

EDITMAT matrixname:

The EDITMAT command can also be used to create matrices.

1. Press CMDS

2. Press M 1, and then press .

The Matrix catalog opens with M1 available for editing.

EDITMAT

matrixname is an alternative to opening the matrix editor with matrixname.

This command prevents the display from being updated after the program runs. This allows you to view the graphics created by the program. Cancel FREEZE by pressing any key.

FREEZE:

18-28 Programming


GETKEY

INPUT

MSGBOX

Programming

Waits for a key, then stores the keycode rc.p in name, where r is row number, c is column number, and p is keyplane number. The key-planes numbers are: 1 for unshifted; 2 for shifted; 4 for alpha-shifted; and 5 for both alpha-shifted and shifted.

GETKEY name:

Creates an input form with a title bar and one field. The field has a label and a default value. There is text help at the bottom of the form. The user enters a value and presses the menu key. The value that the user enters is stored in the variable name. The title, label, and help items are text strings and need to be enclosed in double quotes.

Use CHARS to type the quote marks " ".

INPUT name;title,label;help;default:

Example

INPUT R; "Circular Area";

"Radius";

"Enter Number";1:

Displays a message box containing textitem. A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings of text.

For example, "AREA IS:" 2 +2 becomes AREA IS: 4.

Use CHARS to type the quote marks " ".

MSGBOX textitem:

Example

1 A:

MSGBOX "AREA IS: "π*A^2:

You can also use the NoteText variable to provide text arguments. This can be used to insert line breaks. For example, press NOTE and type AREA IS .

The position line

MSGBOX NoteText " " π*A^2: will display the same message box as the previous example.

18-29


PROMPT

WAIT

Displays an input box with name as the title, and prompts for a value for name. name can be a variable such as

A…Z, θ, L1…l9, C1…C9 or Z1…Z9.

PROMPT name:

Halts program execution for the specified number of seconds.

WAIT seconds:

Stat-One and Stat-Two commands

The following commands are used for analyzing onevariable and two-variable statistical data.

Stat-One commands

DO1VSTATS

Calculates STATS using datasetname and stores the results in the corresponding variables: NΣ, TotΣ, MeanΣ,

PVarΣ, SVarΣ, PSDev, SSDev, MinΣ, Q1, Median, Q3, and MaxΣ. Datasetname can be H1, H2, ..., or H5.

Datasetname must include at least two data points.

DO1VSTATS datasetname:

SETFREQ

Sets datasetname frequency according to column or value. Datasetname can be H1, H2,..., or H5, column can be C0–C9 and value can be any positive integer.

SETFREQ datasetname;column: or

SETFREQ definition;value:

SETSAMPLE

Sets datasetname sample according to column.

Datasetname can be H1–H5, and column can be

CO–C9.

SETSAMPLE datasetname;column:

Stat-Two commands

DO2VSTATS

Calculates STATS using datasetname and stores the results in corresponding variables: MeanX, ΣX, ΣX2,

MeanY, ΣY, ΣY2, ΣXY, Corr, PCov, SCov, and RELERR.

18-30 Programming


SETDEPEND

SETINDEP

Datasetname can be SI, S2,..., or S5. Datasetname must include at least two pairs of data points.

DO2VSTATS datasetname:

Sets datasetname dependent column. Datasetname can be S1, S2, …, or S5 and column can be C0–C9.

SETDEPEND datasetname;column:

Sets datasetname independent column. Datasetname can be S1, S2,…, or S5 and column can be C0–C9.

SETINDEP datasetname;column:

Storing and retrieving variables in programs

The hp 39gs has both Home variables and Aplet variables. Home variables are used for real numbers, complex numbers, graphics, lists, and matrices. Home variables keep the same values in HOME and in aplets.

Aplet variables are those whose values depend on the current aplet. The aplet variables are used in programming to emulate the definitions and settings you make when working with aplets interactively.

You use the Variable menu ( ) to retrieve either

Home variables or aplet variables. See “The VARS menu” on page 14-4. Not all variables are available in every

aplet. S1fit–S5fit, for example, are only available in the

Statistics aplet. Under each variable name is a list of the aplets where the variable can be used.

Programming 18-31


Plot-view variables

Area

Function

Axes

All Aplets

Contains the last value found by the Area function in Plot-

FCN menu.

Connect

Function

Parametric

Polar

Solve

Statistics

Turns axes on or off.

From Plot Setup, check (or uncheck) AXES.

or

In a program, type:

1 Axes—to turn axes on (default).

0 Axes—to turn axes off.

Draws lines between successively plotted points.

From Plot Setup, check (or uncheck) CONNECT.

or

In a program, type

1 Connect—to connect plotted points (default, except in Statistics where the default is off).

0 Connect—not to connect plotted points.

Coord

Function

Parametric

Polar

Sequence

Solve

Statistics

Turns the coordinate-display mode in Plot view on or off.

From Plot view, use the Menu mean key to toggle coordinate display on an off.

In a program, type

1 Coord—to turn coordinate display on (default).

0 Coord—to turn coordinate display off.

Extremum

Function

FastRes

Function

Solve

Contains the last value found by the Extremum operation in the Plot-FCN menu.

Toggles resolution between plotting in every other column

(faster), or plotting in every column (more detail).

From Plot Setup, choose Faster or More Detail.

or

In a program, type

1 FastRes—for faster.

0 FastRes—for more detail (default).

18-32 Programming


Grid

All Aplets

Hmin/Hmax

Statistics

Hwidth

Statistics

Indep

All Aplets

InvCross

All Aplets

Programming

Turns the background grid in Plot view on or off. From Plot setup, check (or uncheck) GRID.

or

In a program, type

1 Grid to turn the grid on.

0 Grid to turn the grid off (default).

Defines minimum and maximum values for histogram bars.

From Plot Setup for one-variable statistics, set values for

HRNG.

or

In a program, type n

1

Hmin n

2

Hmax where n

2

> n

1

Sets the width of histogram bars.

From Plot Setup in 1VAR stats set a value for Hwidth or

In a program, type

n Hwidth

Defines the value of the independent variable used in tracing mode.

In a program, type

n Indep

Toggles between solid crosshairs or inverted crosshairs.

(Inverted is useful if the background is solid).

From Plot Setup, check (or uncheck) InvCross or

In a program, type:

1 InvCross—to invert the crosshairs.

0 InvCross —for solid crosshairs (default).

18-33


Isect

Function

Labels

All Aplets

Nmin / Nmax

Sequence

Recenter

All Aplets

Root

Function

Contains the last value found by the Intersection function in the Plot-FCN menu.

Draws labels in Plot view showing X and Y ranges.

From Plot Setup, check (or uncheck) Labels or

In a program, type

1 Labels—to turn labels on.

0 Labels—to turn labels off (default).

Defines the minimum and maximum independent variable values. Appears as the NRNG fields in the Plot Setup input form.

From Plot Setup, enter values for NRNG.

or


1 n

2

Nmin

Nmax where n

2

> n

1

Recenters at the crosshairs locations when zooming.

From Plot-Zoom-Set Factors, check (or uncheck)

Recenter or

In a program, type

1 Recenter— to turn recenter on (default).

0 Recenter—to turn recenter off.

Contains the last value found by the Root function in the

Plot-FCN menu.

18-34 Programming


S1mark–S5mark

Statistics

SeqPlot

Sequence

Simult

Function

Parametric

Polar

Sequence

Slope

Function

StatPlot

Statistics

Sets the mark to use for scatter plots.

From Plot Setup for two-variable statistics, S1mark-

S5mark, then choose a mark.

or

In a program, type n S1mark where n is 1,2,3,...5

Enables you to choose types of sequence plot: Stairstep or Cobweb.

From Plot Setup, select SeqPlot, then choose

Stairstep or Cobweb.

or

In a program, type

1 SeqPlot—for Stairstep.

2 SeqPlot—for Cobweb.

Enables you to choose between simultaneous and sequential graphing of all selected expressions.

From Plot Setup, check (or uncheck) _ SIMULT or

In a program, type

1 Simult—for simultaneous graphing (default).

0 Simult—for sequential graphing.

Contains the last value found by the Slope function in the

Plot-FCN menu.

Enables you to choose types of 1-variable statistics plot between Histogram or Box-and-Whisker.

From Plot Setup, select StatPlot, then choose

Histogram or BoxWhisker.

or

In a program, type

1 StatPlot—for Histogram.

2 StatPlot—for Box-and-Whisker.

Programming 18-35


Umin/Umax

Polar

Ustep

Polar

Tmin / Tmax

Parametric

Tracing

All Aplets

Sets the minimum and maximum independent values.

Appears as the URNG field in the Plot Setup input form.

From the Plot Setup input form, enter values for URNG.

or


1 n

2

Umin

Umax where n

2

> n

1

Sets the step size for an independent variable.

From the Plot Setup input form, enter values for USTEP.

or

In a program, type n Ustep where

Sets the minimum and maximum independent variable values. Appears as the TRNG field in the Plot Setup input form.

From Plot Setup, enter values for TRNG.

or


1

Tmin n

2

Tmax where n

2

> n

1

Turns the tracing mode on or off in Plot view.

In a program, type

1 Tracing—to turn Tracing mode on (default).

0 Tracing—to turn Tracing mode off.

18-36 Programming


Tstep

Parametric

Xcross

All Aplets

Ycross

All Aplets

Xtick

All Aplets

Ytick

All Aplets

Xmin / Xmax

All Aplets

Programming

Sets the step size for the independent variable.

From the Plot Setup input form, enter values for TSTEP.

or

In a program, type n Tstep where

Sets the horizontal coordinate of the crosshairs. Only works with TRACE off.

In a program, type n Xcross

Sets the vertical coordinate of the crosshairs. Only works with TRACE off.

In a program, type n Ycross

Sets the distance between tick marks for the horizontal axis.

From the Plot Setup input form, enter a value for Xtick.

or

In a program, type n Xtick where

Sets the distance between tick marks for the vertical axis.

From the Plot Setup input form, enter a value for Ytick.

or

In a program, type n Ytick where

Sets the minimum and maximum horizontal values of the plot screen. Appears as the XRNG fields (horizontal range) in the Plot Setup input form.

From Plot Setup, enter values for XRNG.

or

In a program, type

18-37


Ymin / Ymax

All Aplets

Xzoom

All Aplets

Yzoom

All Aplets n

1

Xmin n

2

Xmax where n

2

> n

1

Sets the minimum and maximum vertical values of the plot screen. Appears as the YRNG fields (vertical range) in the

Plot Setup input form.

From Plot Setup, enter the values for YRNG.

or


1

Ymin n

2

Ymax where n

2

> n

1

Sets the horizontal zoom factor.

From Plot-ZOOM-Set Factors, enter the value for XZOOM.

or

In a program, type

n XZOOM where

The default value is 4.

Sets the vertical zoom factor.

From Plot-ZOOM-Set Factors, enter the value for YZOOM.

or

In a program, type

n YZOOM

The default value is 4.

18-38 Programming


Symbolic-view variables

Angle

All Aplets

F1...F9, F0

Function

X1, Y1...X9,Y9

X0,Y0

Parametric

R1...R9, R0

Polar

U1...U9, U0

Sequence

E1...E9, E0

Solve

Sets the angle mode.

From Symbolic Setup, choose Degrees, Radians, or

Grads for angle measure.

or

In a program, type

1 Angle —for Degrees.

2 Angle —for Radians.

3 Angle—for Grads.

Can contain any expression. Independent variable is X.

Example

'SIN(X)' F1(X)

You must put single quotes around an expression to keep it from being evaluated before it is stored. Use

CHARS to type the single quote mark.

Can contain any expression. Independent variable is T.

Example

'SIN(4*T)' Y1(T):'2*SIN(6*T)'

X1(T)

Can contain any expression. Independent variable is θ.

Example

'2*SIN(2*θ)' R1(θ)

Can contain any expression. Independent variable is N.

Example

RECURSE (U,U(N-1)*N,1,2) U1(N)

Can contain any equation or expression. Independent variable is selected by highlighting it in Numeric View.

Example

'X+Y*X-2=Y' E1

Programming 18-39


S1fit...S5fit

Statistics

Sets the type of fit to be used by the FIT operation in drawing the regression line.

From Symbolic Setup view, specify the fit in the field for

S1FIT, S2FIT, etc.

or

In a program, store one of the following constant numbers or names into a variable S1fit, S2fit, etc.

1 Linear

2 LogFit

3 ExpFit

4 Power

5 QuadFit

6 Cubic

7 Logist

8 ExpFit

9 TrigFit

10 User Defined

Example

Cubic S2fit or

6 S2fit

18-40 Programming


Numeric-view variables

The following aplet variables control the Numeric view.

The value of the variable applies to the current aplet only.

C1...C9, C0

Statistics

C0 through C9, for columns of data. Can contain lists.

Enter data in the Numeric view or

In a program, type

LIST Cn where n = 0, 1, 2, 3 ... 9

Digits

All Aplets

Number of decimal places to use for Number format in the HOME view and for labeling axes in the Plot view.

From the Modes view, enter a value in the second field of

Number Format.

or

In a program, type

n Digits where

Format

All Aplets

Defines the number display format to use for numeric format in the HOME view and for labeling axes in the Plot view.

From the Modes view, choose Standard, Fixed,

Scientific, Engineering, Fraction or Mixed

Fraction in the Number Format field.

or

In a program, store the constant number (or its name) into the variable Format.

1 Standard

2 Fixed

3 Sci

4 Eng

5 Fraction

6 MixFraction

Programming 18-41


NumCol

All Aplets except

Statistics aplet

NumFont

Function

Parametric

Polar

Sequence

Statistics

NumIndep

Function

Parametric

Polar

Sequence

NumRow

All Aplets except

Statistics aplet

NumStart

Function

Parametric

Polar

Sequence

18-42

Note that if Fraction or Mixed Fraction is chosen, the setting will be ignored when labeling axes in Plot view. A setting of Scientific will be used instead.

Example

Scientific Format or

3 Format

Sets the column to be highlighted in Numeric view.

In a program, type

n NumCol where n can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Enables you to choose the font size in Numeric view.

Does not appear in the Num Setup input form.

Corresponds to the key in Numeric view.

In a program, type

0 NumFont for small (default).

1 NumFont for big.

Specifies the list of independent values to be used by

Build Your Own Table.

In a program, type

LIST NumIndep

Sets the row to be highlighted in Numeric view.

In a program, type

n NumRow where

Sets the starting value for a table in Numeric view.

From Num Setup, enter a value for NUMSTART.

or

In a program, type

n NumStart

Programming


NumStep

Function

Parametric

Polar

Sequence

NumType

Function

Parametric

Polar

Sequence

NumZoom

Function

Parametric

Polar

Sequence

StatMode

Statistics

Programming

Sets the step size (increment value) for an independent variable in Numeric view.

From Num Setup, enter a value for NUMSTEP.

or

In a program, type

n NumStep where

Sets the table format.

From Num Setup, choose Automatic or Build Your

Own.

or

In a program, type

0 NumType for Build Your Own.

1 NumType for Automatic (default).

Sets the zoom factor in the Numeric view.

From Num Setup, type in a value for NUMZOOM.

or

In a program, type

n NumZoom where

Enables you to choose between 1-variable and 2-variable statistics in the Statistics aplet. Does not appear in the Plot

Setup input form. Corresponds to the menu keys in Numeric View.

and

In a program, store the constant name (or its number) into the variable StatMode. 1VAR =1, 2VAR=2.

Example

1VAR StatMode or

1 StatMode

18-43


Note variables

NoteText

All Aplets

The following aplet variable is available in Note view.

Use NoteText to recall text previously entered in Note view.

Sketch variables

The following aplet variables are available in Sketch view.

Page

All Aplets

Sets a page in a sketch set. The graphics can be viewed one at a time using the and keys.

The Page variable refers to the currently displayed page of a sketch set.

In a program, type

graphicname Page

PageNum

All Aplets

Sets a number for referring to a particular page of the sketch set (in Sketch view).

In a program, type the page that is shown when

SKETCH is pressed.

n PageNum


19

Extending aplets

Aplets are the application environments where you explore different classes of mathematical operations.

You can extend the capability of the HP 39gs in the following ways:

• Create new aplets, based on existing aplets, with specific configurations such as angle measure, graphical or tabular settings, and annotations.

• Transmit aplets between HP 39gs calculators via an infra red link.

• Download e-lessons (teaching aplets) from

Hewlett-Packard’s Calculator web site.

•

Program new aplets. See chapter 18,

“Programming”, for further details.

Creating new aplets based on existing aplets

You can create a new aplet based on an existing aplet.

To create a new aplet, save an existing aplet under a new name, then modify the aplet to add the configurations and the functionality that you want.

Information that defines an aplet is saved automatically as it is entered into the calculator.

To keep as much memory available for storage as possible, delete any aplets you no longer need.

Example

This example demonstrates how to create a new aplet by saving a copy of the built-in Solve aplet. The new aplet is saved under the name “TRIANGLES” contains the formulas commonly used in calculations involving right-angled triangles.

Extending aplets 19-1


1. Open the Solve aplet and save it under the new name.

Solve

|

T R I A N G L E S

2. Enter the four formulas:

H

θ

O

θ

A

H

θ

O

A

A

C

B

3. Decide whether you want the aplet to operate in

Degrees, Radians, or Grads.

MODES

Degrees

4. View the Aplet Library. The “TRIANGLES” aplet is listed in the Aplet Library.

The Solve aplet can now be reset and used for other problems.

19-2 Extending aplets


Using a customized aplet

To use the “Triangles” aplet, simply select the appropriate formula, change to the Numeric view and solve for the missing variable.

Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 o

with the horizontal and extends 5 metres up the wall.

1. Select the aplet.

TRIANGLES

2. Choose the sine formula in E1.

3. Change to the Numeric view and enter the known values.

35

5

4. Solve for the missing value.

The length of the ladder is approximately 8.72 metres

Resetting an aplet

Resetting an aplet clears all data and resets all default settings.

To reset an aplet, open the Library, select the aplet and press .

You can only reset an aplet that is based on a built-in aplet if the programmer who created it has provided a

Reset option.

Extending aplets 19-3


Annotating an aplet with notes

The Note view ( NOTE ) attaches a note to the current

aplet. See Chapter 17, “Notes and sketches”.

Annotating an aplet with sketches

The Sketch view ( SKETCH ) attaches a picture to the

current aplet. See chapter 17, “Notes and sketches”.

H I N T Notes and sketches that you attach to an aplet become part of the aplet. When you transfer the aplet to another calculator, the associated note and sketch are transferred as well.

Downloading e-lessons from the web

In addition to the standard aplets that come with the calculator, you can download aplets from the world wide web. For example, Hewlett-Packard’s Calculators web site contains aplets that demonstrate certain mathematical concepts. Note that you need the Graphing Calculator

Connectivity Kit in order to load aplets from a PC.

Hewlett-Packard’s Calculators web site can be found at: http://www.hp.com/calculators

Sending and receiving aplets

A convenient way to distribute or share problems in class and to turn in homework is to transmit (copy) aplets directly from one HP 39gs to another. This can take place via the infrared port or via a suitable cable. (You can use a serial cable with a 4-pin mini-USB connector, which plugs into the RS232 port on the calculator. The serial cable is available as a separate accessory.)

You can also send aplets to, and receive aplets from, a

PC. This requires special software running on the PC (such as the PC Connectivity Kit). A USB cable with a 5-pin mini-

USB connector is provided with the hp39gs for connecting with a PC. It plugs into the USB port on the calculator.



To transmit an aplet

Extending aplets

1. Connect the PC or aplet disk drive to the calculator by cable or align the two calculators’ infrared ports by matching up the triangle marks on the rims of the calculators.

Place the calculators no more than 4 inches (10 cm) apart.

2. Sending calculator: Open the Library, highlight the aplet to send, and press .

– The

SEND TO

menu appears with the following options:

HP39G (IRDA)

= to send via high-speed infrared

HP39/40 (USB)

= to send via the USB port

HP39/40 (SER)

= to send via the RS232 serial port

USB DISK DRIVE

= to send to a disk drive via the USB port

SER. DISK DRIVE

= to send to a disk drive via the

RS232 serial port

Note: choose a disk drive option if you are using the hp39gs connectivity kit to transfer the aplet.

Highlight your selection and press .

– If transmitting to a disk drive, you have the options of sending to the current (default) directory or to another directory.

3. Receiving calculator: Open the aplet library and press .

– The

RECEIVE FROM menu appears with the following options:

HP39G (IRDA)

= to receive via high-speed infrared

HP39G

= to receive via low-speed infrared

HP39/40 (USB)

= to receive via the USB port

HP39/40 (SER)

= to receive via the RS232 serial port

USB DISK DRIVE

= to receive from a disk drive via the

USB port

SER. DISK DRIVE

= to receive from a disk drive via the

RS232 serial port

19-5


Note: choose a disk drive option if you are using the hp39gs connectivity kit to transfer the aplet.

Highlight your selection and press .

The Transmit annunciator— —is displayed until transmission is complete.

If you are using the PC Connectivity Kit to download aplets from a PC, you will see a list of aplets in the PC’s current directory. Check as many items as you would like to receive.

Sorting items in the aplet library menu list

Once you have entered information into an aplet, you have defined a new version of an aplet. The information is automatically saved under the current aplet name, such as “Function.” To create additional aplets of the same type, you must give the current aplet a new name.

The advantage of storing an aplet is to allow you to keep a copy of a working environment for later use.

The aplet library is where you go to manage your aplets.

Press . Highlight (using the arrow keys) the name of the aplet you want to act on.

To sort the aplet list

In the aplet library, press and press .

. Select the sorting scheme

• Chronologically produces a chronological order based on the date an aplet was last used. (The lastused aplet appears first, and so on.)

• Alphabetically produces an alphabetical order by aplet name.

To delete an aplet

You cannot delete a built-in aplet. You can only clear its data and reset its default settings.

To delete a customized aplet, open the aplet library, highlight the aplet to be deleted, and press delete all custom aplets, press CLEAR .

. To



R

Reference information

Glossary

aplet command expression function

HOME

Library

A small application, limited to one topic. The built-in aplet types are

Function, Parametric, Polar,

Sequence, Solve, Statistics,

Inference, Finance, Trig Explorer,

Quad Explorer, Linear Solver and

Triangle Solve. An aplet can be filled with the data and solutions for a specific problem. It is reusable (like a program, but easier to use) and it records all your settings and definitions.

An operation for use in programs.

Commands can store results in variables, but do not display results.

Arguments are separated by semicolons, such as DISP expression ;line#.

A number, variable, or algebraic expression (numbers plus functions) that produces a value.

An operation, possibly with arguments, that returns a result. It does not store results in variables. The arguments must be enclosed in parentheses and separated with commas (or periods in Comma mode), such as

CROSS(matrix1,matrix2).

The basic starting point of the calculator. Go to HOME to do calculations.

For aplet management: to start, save, reset, send and receive aplets.

R-1

HP 39gs English.book Page 2 Wednesday, December 7, 2005 11:24 PM list matrix menu menu keys note program sketch variable vector

A set of values separated by commas

(periods if the Decimal Mark mode is set to Comma) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values.

Created and manipulated by the List editor and catalog.

A two-dimensional array of values separated by commas (periods if the

Decimal Mark mode is set to Comma) and enclosed in nested brackets.

Created and manipulated by the

Matrix catalog and editor. Vectors are also handled by the Matrix catalog and editor.

A choice of options given in the display. It can appear as a list or as a set of menu-key labels across the bottom of the display.

The top row of keys. Their operations depend on the current context. The labels along the bottom of the display show the current meanings.

Text that you write in the Notepad or in the Note view for a specific aplet.

A reusable set of instructions that you record using the Program editor.

A drawing that you make in the

Sketch view for a specific aplet.

The name of a number, list, matrix, note, or graphic that is stored in memory. Use

to retrieve.

to store and use

A one-dimensional array of values separated by commas (periods if the

Decimal Mark mode is set to Comma) and enclosed in single brackets.

Created and manipulated by the

Matrix catalog and editor.

R-2

ReferenceInfo.fm Page 3 Friday, December 16, 2005 10:00 AM views The possible contexts for an aplet:

Plot, Plot Setup, Numeric, Numeric

Setup, Symbolic, Symbolic Setup,

Sketch, Note, and special views like split screens.

Resetting the HP 39gs

If the calculator “locks up” and seems to be stuck, you must reset it. This is much like resetting a PC. It cancels certain operations, restores certain conditions, and clears temporary memory locations. However, it does not clear stored data (variables, aplet databases, programs) unless you use the procedure, “To erase all memory and reset defaults”.

To reset using the keyboard

Press and hold the key and the third menu key simultaneously, then release them.

If the calculator does not respond to the above key sequence, then:

1. Turn the calculator over and locate the small hole in the back of the calculator.

2. Insert the end of a straightened metal paper clip into the hole as far as it will go. Hold it there for 1 second, then remove it.

3. Press If necessary, press and the first and last menu keys simultaneously. (Note: This will erase your calculator memory.)

To erase all memory and reset defaults

If the calculator does not respond to the above resetting procedures, you might need to restart it by erasing all of memory. You will lose everything you have stored. All factory-default settings are restored.

1. Press and hold the key, the first menu key, and the last menu key simultaneously.

2. Release all keys in the reverse order.

Note: To cancel this process, release only the top-row keys, then press the third menu key.

R-3

ReferenceInfo.fm Page 4 Friday, December 16, 2005 10:00 AM

If the calculator does not turn on

If the HP 39gs does not turn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure. If the calculator still does not turn on, please contact Customer Support for further information.

1. Press and hold the key for 10 seconds.

2. Press and hold the key and the third menu key simultaneously. Release the third menu key, then release the key.

3. Press and hold the key, the first menu key, and the sixth menu key simultaneously. Release the sixth menu key, then release the first menu key, and then release the key.

4. Locate the small hole in the back of the calculator.

Insert the end of a straightened metal paper clip into the hole as far as it will go. Hold it there for 1 second, then remove it. Press the key.

5. Remove the batteries (see “Batteries” on page R-4),

press and hold the key for 10 seconds, and then put the batteries back in. Press the key.

Operating details

Operating temperature: 0° to 45°C (32° to 113°F).

Storage temperature: –20° to 65°C (– 4° to 149°F).

Operating and storage humidity: 90% relative humidity at 40°C (104°F) maximum. Avoid getting the calculator wet.

Battery operates at 6.0V dc, 80mA maximum.

Batteries

The calculator uses 4 AAA(LR03) batteries as main power and a CR2032 lithium battery for memory backup.

Before using the calculator, please install the batteries according to the following procedure.

R-4

ReferenceInfo.fm Page 5 Friday, December 16, 2005 10:00 AM

To install the main batteries

a. Slide up the battery compartment cover as illustrated.

b. Insert 4 new AAA (LR03) batteries into the main compartment. Make sure each battery is inserted in the indicated direction.

To install the backup battery

a. Press down the holder. Push the plate to the shown direction and lift it.

b. Insert a new CR2032 lithium battery. Make sure its positive (+) side is facing up.

c. Replace the plate and push it to the original place.

After installing the batteries, press on.

to turn the power

Warning: It is recommended that you replace this battery every 5 years. When the low battery icon is displayed, you need to replace the batteries as soon as possible.

However, avoid removing the backup battery and main batteries at the same time to avoid data lost.

R-5


Variables

Home variables

The home variables are:

Category

Complex

Graphic

Library

List

Matrix

Modes

Notepad

Program

Real

Available name

Z1...Z9, Z0

G1...G9, G0

Function

Parametric

Polar

Sequence

Solve

Statistics

User-named

L1...L9, L0

M1...M9, M0

Ans

Date

HAngle

HDigits

HFormat

Ierr

Time

User-named

Editline

User-named

A...Z, θ

R-6


Function aplet variables

The function aplet variables are:

Category

Plot

Plot-FCN

Symbolic

Numeric

Note

Sketch

Available name

Axes

Connect

Coord

FastRes

Grid

Indep

InvCross

Labels

Recenter

Simult

Tracing

Area

Extremum

Isect

Angle

F1

F2

F3

F4

F5

Digits

Format

NumCol

NumFont

NumIndep

NoteText

Page

Xcross

Ycross

Xtick

Ytick

Xmin

Xmax

Ymin

Ymax

Xzoom

Yxoom

Root

Slope

F6

F7

F8

F9

F0

NumRow

NumStart

NumStep

NumType

NumZoom

PageNum

R-7


Parametric aplet variables

The parametric aplet variables are:

Category

Plot

Available name

Axes

Connect

Coord

Grid

Indep

InvCross

Labels

Recenter

Simult

Tmin

Tmax

Symbolic

Numeric

Note

Sketch

Y2

X3

Y3

X4

Angle

X1

Y1

X2

Y4

X5

Digits

Format

NumCol

NumFont

NumIndep

NoteText

Page

Y7

X8

Y8

X9

Y5

X6

Y6

X7

Y9

X0

Y0

Tracing

Tstep

Xcross

Ycross

Xtick

Ytick

Xmin

Xmax

Ymin

Ymax

Xzoom

Yzoom

NumRow

NumStart

NumStep

NumType

NumZoom

PageNum

R-8


Polar aplet variables

The polar aplet variables are:

Category

Plot

Symbolic

Numeric

Note

Sketch

Available names

Axes

Connect

Coord

Grid

Indep

InvCross

Labels

Recenter

Simult

Umin

Umax

θstep

Tracing

Angle

R1

R2

R3

R4

R5

Digits

Format

NumCol

NumFont

NumIndep

NoteText

Page

R6

R7

R8

R9

R0

Xcross

Ycross

Xtick

Ytick

Xmin

Xmax

Ymin

Ymax

Xzoom

Yxoom

NumRow

NumStart

NumStep

NumType

NumZoom

PageNum

R-9


Sequence aplet variables

The sequence aplet variables are:

Category

Plot

Symbolic

Numeric

Note

Sketch

Available name

Axes

Coord

Grid

Indep

InvCross

Labels

Nmin

Nmax

Recenter

SeqPlot

Simult

Angle

U1

U2

U3

U4

U5

Digits

Format

NumCol

NumFont

NumIndep

NoteText

Page

U6

U7

U8

U9

U0

Tracing

Xcross

Ycross

Xtick

Ytick

Xmin

Xmax

Ymin

Ymax

Xzoom

Yzoom

NumRow

NumStart

NumStep

NumType

NumZoom

PageNum

R-10


Solve aplet variables

The solve aplet variables are:

Category

Plot

Symbolic

Numeric

Note

Sketch

Available name

Axes

Connect

Coord

FastRes

Grid

Indep

InvCross

Labels

Recenter

Tracing

Angle

E1

E2

E3

E4

E5

Digits

Format

NoteText

Page

E6

E7

E8

E9

E0

Xcross

Ycross

Xtick

Ytick

Xmin

Xmax

Ymin

Ymax

Xzoom

Yxoom

NumCol

NumRow

PageNum

R-11


Statistics aplet variables

The statistics aplet variables are:

Category

Plot

Symbolic

Numeric

Stat-One

Stat-Two

Note

Sketch

C0,...C9

Digits

Format

NumCol

MaxΣ

MeanΣ

Median

MinΣ

NΣ

Q1

Corr

Cov

Fit

MeanX

MeanY

RelErr

NoteText

Page

Available name

Axes

Connect

Coord

Grid

Hmin

Hmax

Hwidth

Indep

InvCross

Labels

Recenter

S1mark

S2mark

S3mark

Angle

S1fit

S2fit

PageNum

Q3

PSDev

SSDev

PVarΣ

SVarΣ

TotΣ

ΣX

ΣX2

ΣXY

ΣY

ΣY2

S4mark

S5mark

StatPlot

Tracing

Xcross

Ycross

Xtick

Ytick

Xmin

Xmax

Ymin

Ymax

Xzoom

Yxoom

S3fit

S4fit

S5fit

NumFont

NumRow

StatMode

R-12


MATH menu categories

Math functions

The math functions are:

Category

Calculus

Complex

Constant

Available name

∂

∫

TAYLOR e i

ARG

CONJ

Hyperb.

List

Loop

ACOSH

ASINH

ATANH

COSH

SINH

CONCAT

ΔLIST

MAKELIST

πLIST

POS

ITERATE

RECURSE

Σ

IM

RE

MAXREAL

MINREAL

π

TANH

ALOG

EXP

EXPM1

LNP1

REVERSE

SIZE

ΣLIST

SORT

R-13


Category

Matrix

Polynom.

Prob.

Real

Stat-Two

Symbolic

CEILING

DEG→RAD

FLOOR

FNROOT

FRAC

HMS→

→HMS

INT

MANT

MAX

PREDX

PREDY

=

ISOLATE

LINEAR?

Available name (Continued)

COLNORM

COND

CROSS

DET

DOT

EIGENVAL

EIGENVV

IDENMAT

INVERSE

LQ

LSQ

LU

MAKEMAT

QR

RANK

ROWNORM

RREF

SCHUR

SIZE

SPECNORM

SPECRAD

SVD

SVL

TRACE

TRN

POLYCOEF

POLYEVAL

COMB

!

PERM

RANDOM

POLYFORM

POLYROOT

UTPC

UTPF

UTPN

UTPT

MIN

MOD

%

%CHANGE

%TOTAL

RAD→DEG

ROUND

SIGN

TRUNCATE

XPON

QUAD

QUOTE

|

R-14


Category

Tests

Trig

≠

>

≥

<

≤

= =

Available name (Continued)

AND

IFTE

NOT

OR

XOR

ACOT

ACSC

ASEC

COT

CSC

SEC

Program constants

The program constants are:

Category

Angle

Format

Available name

Degrees

Grads

Radians

Standard

Fixed

SeqPlot

S1...5fit

StatMode

StatPlot

Sci

Eng

Fraction

Cobweb

Stairstep

Linear

LogFit

ExpFit

Power

Trigonometric

Stat1Var

Stat2Var

Hist

BoxW

QuadFit

Cubic

Logist

User

Exponent

R-15


Physical Constants

The physical constants are:

Category

Chemist

Phyics

Quantum

Available Name

• Avogadro (Avogadro’s Number,

NA)

• Boltz. (Boltmann, k)

• mol. vo... (molar volume, Vm)

• univ gas (universal gas, R)

• std temp (standard temperature,

St dT)

• std pres (standard pressure,

St dP)

• StefBolt (Stefan-Boltzmann, σ)

• l ight s... (speed of light, c)

• permitti (permittivity, ε0)

• permeab (permeability, μ0)

• acce gr... (acceleration of gravity, g)

• gravita... (gravitation, G)

• Plank’s (Plank’s constant, h)

• Dirac’s (Dirac’s, hbar)

• e charge (electronic charge, q)

• e mass (electron mass, me)

• q/me ra... (q/me ratio, qme)

• proton m (proton mass, mp)

• mp/me r... (mp/me ratio, mpme)

• fine str (fine structure, α)

• mag flux (magnetic flux, φ)

• Faraday (Faraday, F)

• Rydberg (Rydberg, R ∞ )

• Bohr rad (Bohr radius, a0)

• Bohr mag (Bohr magneton, μB)

• nuc. mag (nuclear magneton,

μN)

• photon... (photon wavelength,

λ)

• photon... (photon frequency, f0)

• Compt w... (Compton wavelength, λc)

R-16


Program commands

The program commands are:

Category

Aplet

Branch

Drawing

Graphic

Loop

Matrix

Command

CHECK

SELECT

SETVIEWS

UNCHECK

IF

THEN

ELSE

END

ARC

BOX

ERASE

FREEZE

DISPLAY→

→DISPLAY

→GROB

GROBNOT

GROBOR

GROBXOR

FOR

=

TO

STEP

END

DO

ADDCOL

ADDROW

DELCOL

DELROW

EDITMAT

RANDMAT

Print

Prompt

Stat-One

PRDISPLAY

PRHISTORY

PRVAR

BEEP

CHOOSE

CLRVAR

DISP

DISPXY

DISPTIME

EDITMAT

DO1VSTATS

RANDSEED

CASE

IFERR

RUN

STOP

LINE

PIXOFF

PIXON

TLINE

MAKEGROB

PLOT→

→PLOT

REPLACE

SUB

ZEROGROB

UNTIL

END

WHILE

REPEAT

END

BREAK

REDIM

REPLACE

SCALE

SCALEADD

SUB

SWAPCOL

SWAPROW

FREEZE

GETKEY

INPUT

MSGBOX

PROMPT

WAIT

SETFREQ

SETSAMPLE

R-17


Category

Stat-Two

Command (Continued)

DO2VSTATS

SETDEPEND

SETINDEP

Status messages

Message

Bad Argument

Type

Bad Argument

Value

Infinite Result

Insufficient

Memory

Insufficient

Statistics Data

Meaning

Incorrect input for this operation.

The value is out of range for this operation.

Math exception, such as 1/0.

You must recover some memory to continue operation. Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not builtin) aplets (using

MEMORY ).

Not enough data points for the calculation. For two-variable statistics there must be two columns of data, and each column must have at least four numbers.

Invalid Dimension Array argument had wrong dimensions.

Invalid Statistics

Data

Need two columns with equal numbers of data values.

R-18


Message

Invalid Syntax

Name Conflict

No Equations

Checked

(OFF SCREEN)

Receive Error

Too Few

Arguments

Undefined Name

Undefined Result

Out of Memory


The function or command you entered does not include the proper arguments or order of arguments. The delimiters

(parentheses, commas, periods, and semi-colons) must also be correct. Look up the function name in the index to find its proper syntax.

The | (where) function attempted to assign a value to the variable of integration or summation index.

You must enter and check an equation (Symbolic view) before evaluating this function.

Function value, root, extremum, or intersection is not visible in the current screen.

Problem with data reception from another calculator. Resend the data.

The command requires more arguments than you supplied.

The global variable named does not exist.

The calculation has a mathematically undefined result

(such as 0/0).

You must recover a lot of memory to continue operation.

Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not builtin) aplets (using

MEMORY ).

R-19



Limited Warranty

HP 39gs Graphing Calculator; Warranty period: 12 months

1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective. Replacement products may be either new or like-new.

2. HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase, for the period specified above, due to defects in material and workmanship when properly installed and used. If HP receives notice of such defects during the warranty period, HP will replace software media which does not execute its programming instructions due to such defects.

3. HP does not warrant that the operation of HP products will be uninterrupted or error free. If HP is unable, within a reasonable time, to repair or replace any product to a condition as warranted, you will be entitled to a refund of the purchase price upon prompt return of the product with proof of purchase.

4. HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use.

5. Warranty does not apply to defects resulting from (a) improper or inadequate maintenance or calibration,

(b) software, interfacing, parts or supplies not supplied by HP, (c) unauthorized modification or misuse, (d) operation outside of the published environmental specifications for the product, or (e) improper site preparation or maintenance.

W-1


6. HP MAKES NO OTHER EXPRESS WARRANTY OR

CONDITION WHETHER WRITTEN OR ORAL. TO

THE EXTENT ALLOWED BY LOCAL LAW, ANY

IMPLIED WARRANTY OR CONDITION OF

MERCHANTABILITY, SATISFACTORY QUALITY, OR

FITNESS FOR A PARTICULAR PURPOSE IS LIMITED

TO THE DURATION OF THE EXPRESS WARRANTY

SET FORTH ABOVE. Some countries, states or provinces do not allow limitations on the duration of an implied warranty, so the above limitation or exclusion might not apply to you. This warranty gives you specific legal rights and you might also have other rights that vary from country to country, state to state, or province to province.

7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE

REMEDIES IN THIS WARRANTY STATEMENT ARE

YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS

INDICATED ABOVE, IN NO EVENT WILL HP OR ITS

SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR

DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL

(INCLUDING LOST PROFIT OR DATA), OR OTHER

DAMAGE, WHETHER BASED IN CONTRACT, TORT,

OR OTHERWISE. Some countries, States or provinces do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you.

8. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. HP shall not be liable for technical or editorial errors or omissions contained herein.

FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND

NEW ZEALAND: THE WARRANTY TERMS CONTAINED

IN THIS STATEMENT, EXCEPT TO THE EXTENT

LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT

OR MODIFY AND ARE IN ADDITION TO THE

MANDATORY STATUTORY RIGHTS APPLICABLE TO THE

SALE OF THIS PRODUCT TO YOU.

W-2


Service

Europe Country :

Austria

Belgium

Denmark

Eastern Europe countries

Finland

France

Germany

Greece

Holland

Italy

Norway

Portugal

Telephone numbers

+43-1-3602771203

+32-2-7126219

+45-8-2332844

+420-5-41422523

+35-89640009

+33-1-49939006

+49-69-95307103

+420-5-41422523

+31-2-06545301

+39-02-75419782

+47-63849309

+351-229570200

Spain

Sweden

Switzerland

+34-915-642095

+46-851992065

+41-1-4395358

(German)

+41-22-8278780

(French)

+39-02-75419782

(Italian)

+420-5-41422523 Turkey

UK +44-207-4580161

Czech Republic +420-5-41422523

South Africa +27-11-2376200

Luxembourg +32-2-7126219

Other European countries

+420-5-41422523

Asia Pacific Country : Telephone numbers

Australia

Singapore

+61-3-9841-5211

+61-3-9841-5211

W-3


L.America

Country:

Argentina

Brazil

Mexico

Venezuela

Chile

Columbia

Peru

Central

America &

Caribbean

Guatemala

Puerto Rico

Costa Rica


0-810-555-5520

Sao Paulo 3747-7799;

ROTC 0-800-157751

Mx City 5258-9922;

ROTC 01-800-472-6684

0800-4746-8368

800-360999

9-800-114726

0-800-10111

1-800-711-2884

1-800-999-5105

1-877-232-0589

0-800-011-0524

N.America Country :

U.S.


1800-HP INVENT

Canada (905) 206-4663 or

800- HP INVENT

ROTC = Rest of the country

Please logon to http://www.hp.com for the latest service and support information.h

W-4


Regulatory information

Federal

Communications

Commission Notice

Modifications

Cables

Declaration of

Conformity for

Products Marked with FCC Logo,

United States Only

This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications.

However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures:

• Reorient or relocate the receiving antenna.

• Increase the separation between the equipment and the receiver.

• Connect the equipment into an outlet on a circuit different from that to which the receiver is connected.

• Consult the dealer or an experienced radio or television technician for help.

The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett-Packard Company may void the user's authority to operate the equipment.

Connections to this device must be made with shielded cables with metallic RFI/EMI connector hoods to maintain compliance with FCC rules and regulations.

This device complies with Part 15 of the FCC Rules.

Operation is subject to the following two conditions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation.

For questions regarding your product, contact:


P. O. Box 692000, Mail Stop 530113

W-5


Canadian Notice

Avis Canadien

European Union

Regulatory Notice

Houston, Texas 77269-2000

Or, call

1-800-474-6836

For questions regarding this FCC declaration, contact:


P. O. Box 692000, Mail Stop 510101

Houston, Texas 77269-2000

Or, call

1-281-514-3333

To identify this product, refer to the part, series, or model number found on the product.

This Class B digital apparatus meets all requirements of the Canadian Interference-Causing Equipment

Regulations.

Cet appareil numérique de la classe B respecte toutes les exigences du Règlement sur le matériel brouilleur du

Canada.

This product complies with the following EU Directives:

• Low Voltage Directive 73/23/EEC

• EMC Directive 89/336/EEC

Compliance with these directives implies conformity to applicable harmonized European standards (European

Norms) which are listed on the EU Declaration of

Conformity issued by Hewlett-Packard for this product or product family.

This compliance is indicated by the following conformity marking placed on the product:

Japanese Notice

This marking is valid for non-Telecom prodcts and EU harmonized

Telecom products (e.g. Bluetooth).

xxxx*

This marking is valid for EU non-harmonized Telecom products.

*Notified body number (used only if applicable - refer to the product label)

この装置は、情報処理装置等電波障害自主規制協議会

（VCCI）の基準に基づくクラス B 情報技術装置です。この装

置は、家庭環境で使用することを目的としていますが、この

装置がラジオやテレビジョン受信機に近接して使用されると、

受信障害を引き起こすことがあります。

取り扱い説明書に従って正しい取り扱いをしてください。

W-6


Korean Notice

Disposal of Waste

Equipment by Users in Private

Household in the

European Union

This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your waste equipment for recycling, please contact your local city office, your household waste disposal service or the shop where you purchased the product.

W-7



Index

A

absolute value

13-5

add

13-3

algebraic entry

1-19

alpha characters typing

1-6

alphabetical sorting

19-6

angle measure

1-10

in statistics

10-12

setting

1-11

animation

17-5

creating

17-5

annunciators

1-3

Ans (last answer)

1-24

antilogarithm

13-4

,

13-9

aplet attaching notes

19-4

clearing

19-3

copying

19-4

definition of

R-1

deleting

19-6

Function

13-21

Inference

11-1

key

1-4

library

19-6

Linear Solver

8-1

opening

1-16

Parametric

4-1

Polar

5-1

receiving

19-5

resetting

19-3

sending

19-4

,

19-5

Sketch view

17-1

Solve

7-1

sorting

19-6

statistics

10-1

transmitting

19-5

Triangle Solver

9-1

aplet commands

CHECK

18-14

SELECT

18-14

SETVIEWS

18-17

UNCHECK

18-17

aplet variables definition

14-1

,

14-8

in Plot view

18-32

new

14-1

aplet views canceling operations in

1-1

changing

1-19

note

1-18

Numeric view

1-17

Plot view

1-16

sketch

1-18

split-screen

1-17

Symbolic view

1-16

arc cosecant

13-20

arc cosine

13-4

arc cotangent

13-19

arc secant

13-20

arc sine

13-4

arc tangent

13-5

area graphical

3-10

interactive

3-10

variable

18-32

arguments with matrices

15-10

attaching a note to an aplet

17-1

a sketch to an aplet

17-3

auto scale

2-14

axes plotting

2-7

variable

18-32

B

bad argument

R-18

bad guesses error message

7-7

batteries

R-4

box-and-whisker plot

10-16

branch commands

CASE...END

18-18

IF...THEN...ELSE...END

18-18

IFERR...THEN...ELSE

18-18

branch structures

18-17

build your own table

2-19

I-1


C

calculus operations

13-7

catalogs

1-30

chronological sorting

19-6

circle drawing

17-4

clearing aplet

19-3

characters

1-22

display

1-22

display history

1-25

edit line

1-22

lists

16-6

plot

2-7

cobweb graph

6-1

coefficients polynomial

13-11

columns changing position

18-25

combinations

13-12

commands aplet

18-14

branch

18-17

definition of

R-1

drawing

18-19

graphic

18-21

loop

18-23

print

18-26

program

18-4

,

R-17

stat-one

18-30

stat-two

18-30

with matrices

15-10

complex number functions

13-5

,

13-16

conjugate

13-7

imaginary part

13-7

real part

13-7

complex numbers

1-29

entering

1-29

math functions

13-7

storing

1-29

confidence intervals

11-15

conjugate

13-7

connecting data points

10-19

variable

18-32

via infrared

19-5

via serial cable

19-5

via USB cable

19-5

I-2 connectivity kit

19-4

constant? error message

7-7

constants e

13-8

i

13-8

maximum real number

13-8

minimum real number

13-8

physical

1-8

,

13-25

,

R-16

program

R-15

,

R-16

contrast decreasing display

1-2

increasing display

1-2

conversions

13-8

coordinate display

2-9

copying display

1-22

graphics

17-6

notes

17-8

programs

18-8

correlation coefficient

10-17

CORR

10-17

statistical

10-15

cosecant

13-20

cosine

13-4

inverse hyperbolic

13-9

cotangent

13-20

covariance statistical

10-15

creating aplet

19-1

lists

16-1

matrices

15-3

notes in Notepad

17-6

programs

18-4

sketches

17-3

critical value(s) displayed

11-4

cross product vector

15-11

curve fitting

10-12

,

10-17

D

data set definition

10-8

date, setting

18-28

debugging programs

18-7

decimal changing format

1-10

scaling

2-14

,

2-15

decreasing display contrast

1-2

HP 39gs English.book Page 3 Wednesday, December 7, 2005 11:24 PM definite integral

13-6

deleting aplet

19-6

lists

16-6

matrices

15-5

programs

18-9

statistical data

10-11

delimiters, programming

18-1

derivatives definition of

13-6

in Function aplet

13-22

in Home

13-21

determinant square matrix

15-11

differentiation

13-6

display

18-21

adjusting contrast

1-2

annunciator line

1-2

capture

18-21

clearing

1-2

date and time

18-28

element

15-5

elements

16-4

engineering

1-10

fixed

1-10

fraction

1-10

history

1-22

line

1-23

matrices

15-5

parts of

1-2

printing contents

18-26

rescaling

2-13

scientific

1-10

scrolling through history

1-25

soft key labels

1-2

standard

1-10

divide

13-3

drawing circles

17-4

keys

17-4

lines and boxes

17-3

drawing commands

ARC

18-19

BOX

18-20

ERASE

18-20

FREEZE

18-20

LINE

18-20

PIXOFF

18-20

PIXON

18-20

TLINE

18-20

E

e

13-8

edit line

1-2

editing matrices

15-4

notes

17-2

programs

18-5

Editline

Program catalog

18-2

editors

1-30

eigenvalues

15-11

eigenvectors

15-11

element storing

15-6

E-lessons

1-12

engineering number format

1-11

equals for equations

13-17

logical test

13-19

equations solving

7-1

erasing a line in Sketch view

18-20

error messages bad guesses

7-7

constant?

7-7

exclusive OR

13-19

exiting views

1-19

exponent fit

10-13

minus 1

13-10

of value

13-17

raising to

13-5

expression defining

2-1

,

R-1

entering in HOME

1-19

evaluating in aplets

2-3

literal

13-18

plot

3-3

extremum

3-10

F

factorial

13-12

FastRes variable

18-32

fit a curve to 2VAR data

10-17

choosing

10-12

defining your own

10-13

fixed number format

1-10

I-3

HP 39gs English.book Page 4 Wednesday, December 7, 2005 11:24 PM font size change

3-8

,

17-5

forecasting

10-20

fraction number format

1-11

full-precision display

1-10

function analyze graph with FCN tools

3-4

definition

2-2

,

R-1

entering

1-19

gamma

13-12

intersection point

3-5

math menu

R-13

slope

3-5

syntax

13-2

tracing

2-8

Function aplet

2-20

,

3-1

function variables area

18-32

axes

18-32

connect

18-32

fastres

18-32

grid

18-33

in menu map

R-7

indep

18-33

isect

18-34

labels

18-34

Recenter

18-34

root

18-34

ycross

18-37

G

glossary

R-1

graph analyzing statistical data in

10-19

auto scale

2-14

box-and-whisker

10-16

capture current display

18-21

cobweb

6-1

comparing

2-5

connected points

10-17

defining the independent variable

18-36

drawing axes

2-7

expressions

3-3

grid points

2-7

histogram

10-15

in Solve aplet

7-7

one-variable statistics

10-18

overlaying

2-15

scatter

10-15

,

10-17

I-4 split-screen view

2-14

splitting into plot and close-up

2-13

splitting into plot and table

2-13

stairsteps

6-1

statistical data

10-15

t values

2-6

tickmarks

2-6

tracing

2-8

two-variable statistics

10-18

Graphic commands

→GROB

18-21

DISPLAY→

18-21

GROBNOT

18-21

GROBOR

18-21

GROBXOR

18-22

MAKEGROB

18-22

PLOT→

18-22

REPLACE

18-22

SUB

18-22

ZEROGROB

18-23

graphics copying

17-6

copying into Sketch view

17-6

storing and recalling

17-6

,

18-21

H

histogram

10-15

adjusting

10-16

range

10-18

setting min/max values for bars

18-33

width

10-18

history

1-2

,

18-26

Home

1-1

calculating in

1-19

display

1-2

evaluating expressions

2-4

reusing lines

1-23

variables

14-1

,

14-7

,

R-6

horizontal zoom

18-38

hyperbolic maths functions

13-10

hyperbolic trigonometry

ACOSH

13-9

ALOG

13-9

ASINH

13-9

ATANH

13-9

COSH

13-9

EXP

13-10


EXPM1

13-10

LNP1

13-10

SINH

13-9

TANH

13-9

hypothesis alternative

11-2

inference tests

11-8

null

11-2

tests

11-2

I

i

13-8

implied multiplication

1-20

importing graphics

17-6

notes

17-8

increasing display contrast

1-2

indefinite integral using symbolic variables

13-23

independent values adding to table

2-18

independent variable defined for Tracing mode

18-33

inference confidence intervals

11-15

hypothesis tests

11-8

One-Proportion Z-Interval

11-17

One-Sample Z-Interval

11-15

One-Sample Z-Test

11-8

Two-Proportion Z-Interval

11-17

Two-Proportion Z-Test

11-11

Two-Sample T-Interval

11-19

Two-Sample Z-Interval

11-16

infinite result

R-18

infrared transmission of aplets

19-5

initial guess

7-5

input forms resetting default values

1-9

setting Modes

1-11

insufficient memory

R-18

insufficient statistics data

R-18

integer rank matrix

15-12

integer scaling

2-14

,

2-15

integral definite

13-6

indefinite

13-23

integration

13-6

interpreting intermediate guesses

7-7

intersection

3-11

invalid dimension

R-18

statistics data

R-18

syntax

R-19

inverse hyperbolic cosine

13-9

inverse hyperbolic functions

13-10

inverse hyperbolic sine

13-9

inverse hyperbolic tangent

13-9

inverting matrices

15-8

isect variable

18-34

K

keyboard editing keys

1-5

entry keys

1-5

inactive keys

1-8

list keys

16-2

math functions

1-7

menu keys

1-4

Notepad keys

17-8

shifted keystrokes

1-6

L

labeling axes

2-7

parts of a sketch

17-5

letters, typing

1-6

library, managing aplets in

19-6

linear fit

10-13

Linear Solver aplet

8-1

list arithmetic with

16-7

calculate sequence of elements

16-8

calculating product of

16-8

composed from differences

16-7

concatenating

16-7

counting elements in

16-9

creating

16-1

,

16-3

,

16-4

,

16-5

deleting

16-6

deleting list items

16-3

displaying

16-4

displaying list elements

16-4

editing

16-3

finding statistical values in list elements

16-9

I-5

HP 39gs English.book Page 6 Wednesday, December 7, 2005 11:24 PM generate a series

16-8

list function syntax

16-6

list variables

16-1

returning position of element in

16-8

reversing order in

16-9

sending and receiving

16-6

sorting elements

16-9

storing elements

16-1

,

16-4

,

16-5

storing one element

16-6

logarithm

13-4

logarithmic fit

10-13

functions

13-3

logical operators

AND

13-19

equals (logical test)

13-19

greater than

13-19

greater than or equal to

13-19

IFTE

13-19

less than

13-18

less than or equal to

13-18

NOT

13-19

not equal to

13-19

OR

13-19

XOR

13-19

logistic fit

10-13

loop commands

BREAK

18-24

DO...UNTIL...END

18-23

FOR I=

18-24

WHILE...REPEAT...END

18-23

loop functions

ITERATE

13-10

RECURSE

13-10

summation

13-11

low battery

1-1

lowercase letters

1-6

M

mantissa

13-15

math functions complex number

13-7

hyperbolic

13-10

in menu map

R-13

keyboard

13-3

logical operators

13-18

menu

1-7

polynomial

13-11

probability

13-12

I-6 real-number

13-13

symbolic

13-17

trigonometry

13-19

MATH menu

13-1

math operations

1-19

enclosing arguments

1-21

in scientific notation

1-20

negative numbers in

1-20

matrices adding rows

18-24

addition and subtraction

15-6

arguments

15-10

arithmetic operations in

15-6

assembly from vectors

15-1

changing row position

18-25

column norm

15-10

comma

16-7

commands

15-10

condition number

15-11

create identity

15-13

creating

15-3

creating in Home

15-5

deleting

15-5

deleting columns

18-24

deleting rows

18-24

determinant

15-11

display eigenvalues

15-11

displaying

15-5

displaying matrix elements

15-5

dividing by a square matrix

15-8

dot product

15-11

editing

15-4

extracting a portion

18-25

finding the trace of a square matrix

15-13

inverting

15-8

matrix calculations

15-1

multiplying and dividing by scalar

15-7

multiplying by vector

15-7

multiplying row by value and adding result to second row

18-25

multiplying row number by value

18-25

negating elements

15-8

opening Matrix Editor

18-28

raised to a power

15-7

redimension

18-25

replacing portion of matrix or vector

18-25

sending or receiving

15-4

HP 39gs English.book Page 7 Wednesday, December 7, 2005 11:24 PM singular value decomposition

15-13

singular values

15-13

size

15-12

spectral norm

15-13

spectral radius

15-13

start Matrix Editor

18-24

storing elements

15-3

,

15-5

storing matrix elements

15-6

swap column

18-25

swap row

18-25

transposing

15-13

,

15-14

variables

15-1

matrix functions

15-10

COLNORM

15-10

COND

15-11

CROSS

15-11

DET

15-11

DOT

15-11

EIGENVAL

15-11

EIGENVV

15-11

IDENMAT

15-11

INVERSE

15-11

LQ

15-11

LSQ

15-11

LU

15-12

MAKEMAT

15-12

QR

15-12

RANK

15-12

ROWNORM

15-12

RREF

15-12

SCHUR

15-12

SIZE

15-12

SPECNORM

15-13

SPECRAD

15-13

SVD

15-13

SVL

15-13

TRACE

15-13

TRN

15-13

maximum real number

1-22

,

13-8

memory

R-18

clearing all

R-3

organizing

14-9

out of

R-19

saving

1-25

,

19-1

viewing

14-1

menu lists searching

1-8

minimum real number

13-8

mixed fraction format

1-11

modes angle measure

1-10

decimal mark

1-11

number format

1-10

multiple solutions plotting to find

7-7

multiplication

13-3

implied

1-20

N

name conflict

R-19

naming programs

18-4

natural exponential

13-3

,

13-10

natural log plus 1

13-10

natural logarithm

13-3

negation

13-5

negative numbers

1-20

no equations checked

R-19

Normal Z-distribution, confidence intervals

11-15

note copying

17-8

editing

17-2

importing

17-8

printing

18-26

viewing

17-1

writing

17-1

Notepad

17-1

catalog keys

17-7

creating notes

17-6

writing in

17-6

nrng

2-6

nth root

13-6

null hypothesis

11-2

number format engineering

1-11

fixed

1-10

fraction

1-11

in Solve aplet

7-5

mixed fraction

1-11

scientific

1-10

Standard

1-10

numeric precision

14-9

Numeric view adding values

2-18

automatic

2-16

build your own table

2-19

display defining function for column

2-17

I-7

HP 39gs English.book Page 8 Wednesday, December 7, 2005 11:24 PM recalculating

2-18

setup

2-16

,

2-19

O

off automatic

1-1

power

1-1

on/cancel

1-1

One-Proportion Z-Interval

11-17

One-Sample T-Interval

11-18

One-Sample T-Test

11-12

One-Sample Z-Interval

11-15

One-Sample Z-Test

11-8

order of precedence

1-21

overlaying plots

2-15

,

4-3

P

π

13-8

paired columns

10-11

parametric variables axes

18-32

connect

18-32

grid

18-33

in menu map

R-8

indep

18-33

labels

18-34

recenter

18-34

ycross

18-37

parentheses to close arguments

1-21

to specify order of operation

1-21

pause

18-30

permutations

13-12

pictures attaching in Sketch view

17-3

plot analyzing statistical data in

10-19

auto scale

2-14

box-and-whisker

10-16

cobweb

6-1

comparing

2-5

connected points

10-17

,

10-19

decimal scaling

2-14

defining the independent variable

18-36

drawing axes

2-7

expressions

3-3

grid points

2-7

histogram

10-15

I-8 in Solve aplet

7-7

integer scaling

2-14

one-variable statistics

10-18

overlay plot

2-13

overlaying

2-15

,

4-3

scaling

2-13

scatter

10-15

,

10-17

sequence

2-6

setting up

2-5

,

3-2

split-screen view

2-14

splitting

2-14

splitting into plot and close-up

2-13

splitting into plot and table

2-13

stairsteps

6-1

statistical data

10-15

statistics parameters

10-18

t values

2-6

tickmarks

2-6

to capture current display

18-21

tracing

2-8

trigonometric scaling

2-14

two-variable statistics

10-18

plotting resolution and tracing

2-8

plot-view variables area

18-32

connect

18-32

fastres

18-32

function

18-32

grid

18-33

hmin/hmax

18-33

hwidth

18-33

isect

18-34

labels

18-34

recenter

18-34

root

18-34

s1mark-s5mark

18-35

statplot

18-35

tracing

18-33

umin/umax

18-36

ustep

18-36

polar variables axes

18-32

connect

18-32

grid

18-33

in menu map

R-9

indep

18-33

labels

18-34

recenter

18-34

ycross

18-37

HP 39gs English.book Page 9 Wednesday, December 7, 2005 11:24 PM polynomial coefficients

13-11

evaluation

13-11

form

13-11

roots

13-12

Taylor

13-7

polynomial functions

POLYCOEF

13-11

POLYEVAL

13-11

POLYFORM

13-11

POLYROOT

13-12

ports

19-5

position argument

18-21

power (x raised to y)

13-5

precedence

1-22

predicted values statistical

10-20

print contents of display

18-26

name and contents of variable

18-26

object in history

18-26

variables

18-26

probability functions

!

13-12

COMB

13-12

RANDOM

13-13

UTPC

13-13

UTPF

13-13

UTPN

13-13

UTPT

13-13

program commands

18-4

copying

18-8

creating

18-4

debugging

18-7

deleting

18-9

delimiters

18-1

editing

18-5

naming

18-4

pausing

18-30

printing

18-26

sending and receiving

18-8

structured

18-1

prompt commands beep

18-26

create choose box

18-26

create input form

18-29

display item

18-27

display message box

18-29

halt program execution

18-30

insert line breaks

18-29

prevent screen display being updated

18-28

set date and time

18-28

store keycode

18-29

Q

quadratic extremum

3-6

fit

10-13

function

3-4

quotes in program names

18-4

R

random numbers

13-13

real number maximum

13-8

minimum

13-8

real part

13-7

real-number functions

13-13

%

13-15

%CHANGE

13-15

%TOTAL

13-16

CEILING

13-13

DEGtoRAD

13-14

FNROOT

13-14

HMSto

13-14

INT

13-15

MANT

13-15

MAX

13-15

MIN

13-15

MOD

13-15

RADtoDEG

13-16

ROUND

13-16

SIGN

13-16

TRUNCATE

13-16

XPON

13-17

recalculation for table

2-18

receive error

R-19

receiving aplet

19-5

lists

16-6

matrices

15-4

programs

18-8

redrawing table of numbers

2-17

reduced row echelon

15-12

I-9

HP 39gs English.book Page 10 Wednesday, December 7, 2005 11:24 PM regression analysis

10-17

fit models

10-13

formula

10-12

user-defined fit

10-13

relative error statistical

10-18

resetting aplet

19-3

calculator

R-3

memory

R-3

result copying to edit line

1-22

reusing

1-22

root interactive

3-10

nth

13-6

variable

18-34

root-finding displaying

7-7

interactive

3-9

operations

3-10

variables

3-10

S

S1mark-S5mark variables

18-35

scaling automatic

2-14

decimal

2-10

,

2-14

integer

2-10

,

2-14

,

2-15

options

2-13

resetting

2-13

trigonometric

2-14

scatter plot

10-15

,

10-17

connected

10-17

,

10-19

SCHUR decomposition

15-12

scientific number format

1-10

,

1-20

scrolling in Trace mode

2-8

searching menu lists

1-8

speed searches

1-8

secant

13-20

sending aplets

19-4

lists

16-6

programs

18-8

sequence definition

2-2

I-10 sequence variables

Axes

18-32

Grid

18-33

in menu map

R-10

Indep

18-33

Labels

18-34

Recenter

18-34

Ycross

18-37

serial port connectivity

19-5

setting date

18-28

time

18-28

sign reversal

7-6

sine

13-4

inverse hyperbolic

13-9

singular value decomposition matrix

15-13

singular values matrix

15-13

sketches creating

17-5

creating a blank graphic

18-23

creating a set of

17-5

erasing a line

18-20

labeling

17-5

opening view

17-3

sets

17-5

storing in graphics variable

17-5

slope

3-10

soft key labels

1-2

solve error messages

7-7

initial guesses

7-5

interpreting intermediate guesses

7-7

interpreting results

7-6

plotting to find guesses

7-7

setting number format

7-5

solve variables axes

18-32

connect

18-32

fastres

18-32

grid

18-33

in menu map

R-11

indep

18-33

labels

18-34

recenter

18-34

ycross

18-37

sorting

19-6

aplets in alphabetic order

19-6

HP 39gs English.book Page 11 Wednesday, December 7, 2005 11:24 PM aplets in chronological order

19-6

elements in a list

16-9

spectral norm

15-13

spectral radius

15-13

square root

13-5

stack history printing

18-26

stairsteps graph

6-1

standard number format

1-10

statistics analysis

10-1

analyzing plots

10-19

angle mode

10-12

calculate one-variable

18-30

calculate two-variable

18-30

data set variables

18-41

data structure

18-41

define one-variable sample

18-30

define two-variable data set’s dependent column

18-31

define two-variable data set’s independent column

18-31

defining a fit

10-12

defining a regression model

10-12

deleting data

10-11

editing data

10-10

frequency

18-30

inserting data

10-11

plot type

10-18

plotting data

10-15

predicted values

10-20

regression curve (fit) models

10-12

saving data

10-10

sorting data

10-11

specifying angle setting

10-12

toggling between one-variable and two-variable

10-12

tracing plots

10-19

troubleshooting with plots

10-19

zooming in plots

10-19

statistics variables

Axes

18-32

Connect

18-32

Grid

18-33

Hmin/Hmax

18-33

Hwidth

18-33

in menu map

R-12

Indep

18-33

Labels

18-34

Recenter

18-34

S1mark-S5mark

18-35

Ycross

18-37

step size of independent variable

18-37

storing list elements

16-1

,

16-4

,

16-5

,

16-6

matrix elements

15-3

,

15-5

,

15-6

results of calculation

14-2

value

14-2

strings literal in symbolic operations

13-18

subtract

13-3

summation function

13-11

symbolic calculations in Function aplet

13-21

defining expressions

2-1

differentiation

13-21

displaying definitions

3-8

evaluating variables in view

2-3

setup view for statistics

10-12

symbolic functions

| (where)

13-18

equals

13-17

ISOLATE

13-17

LINEAR?

13-17

QUAD

13-18

QUOTE

13-18

Symbolic view defining expressions

3-2

syntax

13-2

syntax errors

18-7

T

table navigate around

3-8

numeric values

3-7

numeric view setup

2-16

tangent

13-4

inverse hyperbolic

13-9

Taylor polynomial

13-7

θrng

2-6

θstep

2-6

tickmarks for plotting

2-6

time

13-14

I-11

HP 39gs English.book Page 12 Wednesday, December 7, 2005 11:24 PM setting

18-28

time, converting

13-14

times sign

1-20

tmax

18-36

tmin

18-36

too few arguments

R-19

tracing functions

2-8

more than one curve

2-8

not matching plot

2-8

plots

2-8

transmitting lists

16-6

matrices

15-4

programs

18-8

transposing a matrix

15-13

Triangle Solver aplet

9-1

trigonometric fit

10-13

functions

13-19

scaling

2-10

,

2-14

,

2-15

trigonometry functions

ACOT

13-19

ACSC

13-20

ASEC

13-20

COT

13-20

CSC

13-20

SEC

13-20

trng

2-6

truncating values to decimal places

13-16

tstep

2-6

,

18-37

Two-Proportion Z-Interval

11-17

Two-Proportion Z-Test

11-11

Two-Sample T-Interval

11-19

Two-Sample T-test

11-14

Two-Sample Z-Interval

11-16

typing letters

1-6

U

undefined name

R-19

result

R-19

un-zoom

2-11

upper-tail chi-squared probability

13-13

upper-tail normal probability

13-13

I-12 upper-tail Snedecor’s F

13-13

upper-tail student’s t-probability

13-13

USB connectivity

19-5

user defined regression fit

10-13

V

value recall

14-3

storing

14-2

variables aplet

14-1

categories

14-7

clearing

14-3

definition

14-1

,

14-7

,

R-2

in equations

7-10

in Symbolic view

2-3

independent

18-36

local

14-1

previous result (Ans)

1-23

printing

18-26

root

18-34

root-finding

3-10

step size of independent

18-37

types

14-1

,

14-7

use in calculations

14-3

VARS menu

14-4

,

14-5

vectors column

15-1

cross product

15-11

definition of

R-2

views

1-18

configuration

1-18

definition of

R-3

W

warning symbol

1-8

where command ( | )

13-18

X

Xcross variable

18-37

xrng

2-6

Y

Ycross variable

18-37

yrng

2-6


Z

Z-Interval zoom axes box center examples of factors in

2-17

2-9

2-9

11-15

2-12

2-9

2-13

2-11

options

2-9

,

3-8

options within a table

2-17

out

2-9

redrawing table of numbers options

2-17

square

2-10

un-zoom

2-11

within Numeric view

2-17

X-zoom

2-9

Y-zoom

2-10

I-13
