Chapter 9:
Numeric Solver Application
Numeric Solver application lets you obtain the value of any variable in an equation without transforming or simplifying the equation.
Starting up the Numeric Solver displays the Numeric Solver window. The screen to the right shows an example of the window with a sample equation input.
1 Equation input area. Inputting an equation that includes variables and then pressing E will cause 2 and 3 to appear.
2 Equation variables. Input the initial value of each variable to the right of the equals sign (=). Specify the variable you want to solve for by selecting the option button to the left of it.
3 Solution lower limit and upper limit input area*
4 Current convergence range setting*
* Values shown in the sample screen are initial defaults.
1
2
3
4
Numeric Solver Application-Specific Menus and Buttons
• Solve the input equation for the specified variable ...................................................... Solve - Execute or 1
• Clear all single-character variables (a through z)* ....................................................................
a
- Clear a–z
• Initialize the upper boundary and lower boundary ...........................................................
a - Initialize Bound
• Change the convergence range ..........................................................................................
a
- Convergence
* Performing the “Clear a–z” operation clears all single-character variables, regardless of variable data type.
Programs and functions with file names from “a” through “z” are also cleared.
Inputting an Equation
On the Numeric Solver window, input a single equation into the area under “Equation”.
• Use the soft keyboard to input an equation that contains at least one variable.
• If you do not input an equals sign, the calculator assumes that the expression is to the left of the equals sign, and there is a zero to the right.
Solving an Equation
Numeric Solver solves equations by calculating approximations based on Newton’s method. Because of this, you should keep the following points in mind about its solutions.
• Even if an equation has multiple solutions, only one solution is obtained for a particular Numeric Solver operation. For example, x 2 −1 = 0 has the two solutions 1 and −1. Numeric Solver will display either of the solutions first, depending on the value specified by “Lower” and “Upper”.
• Solutions may include errors that are not actual solutions. The accuracy of solutions can be determined by viewing the [Left–Right] value in the Result dialog box. The closer the [Left–Right] value is to zero, the more accurate the results.
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u To solve an equation
1. On the Numeric Solver window, input an equation.
• Here, we will input the equation y = x 2 − 2, and solve for x when y = 0 and y = 2.
2. Press
E
.
3. Input 2 as the values for variable y (to the right of y =).
4. Since we want to solve for x , select the option button to the left of variable x
(so the button next to the variable becomes ).
5. Tap 1 .
• This displays the Result dialog box with the calculation result. Tap [OK] to close the dialog box.
6. Input 0 as the values for variable y (to the right of y =).
7. Tap 1 .
• Though the solution of x 2 − 2 = 0 is x = ± 2, here the value that is displayed is the decimal form of 2, which is near the last solution obtained ( x = 2).
To obtain the other solution, change the Upper value (to 0, for example) and then tap 1 .
0901 t is the time it would take for an object thrown straight up with initial velocity v to reach height h . Use the formula h = vt − 1/2 gt 2 to calculate the initial velocity v for a height of h = 14 meters and a time of t = 2 seconds. Gravitational acceleration is g = 9.8 m/s 2 .
Tip
• If calculator judges that the displayed results are not converging sufficiently, it displays the message “Did not converge.
Do you wish to continue the calculation?” Tap [Yes] to continue, or [No] to cancel the calculation.
• If the message “Can’t solve!” appears on the display, perform either (or both) of the operations below and then tap 1 again.
- Tap a
- [Initialize Bound], or manually change the “Lower” and “Upper” values.
- Change the convergence range. See “To change the convergence range” below.
u To change the convergence range
1. Tap a - [Convergence] to display the Convergence dialog box.
2. Enter an integer in the range of 1 to 13.
• A smaller value increases the allowable error range, and lessens the chance of a “Can’t solve!” error. If a calculation causes a “Can’t solve!” error, try changing this setting to a smaller value.
3. Tap [OK] to apply the setting and close the dialog box.
• The new setting value will be shown in the status bar (page 178 ).
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