RPD-95

Mathematics Application

• RPD-95 Mathematics Library
  • Organization
  • Getting Started
  • Performing Complex Functions
  • Interpolating Points on a Curve
  • Calculating the Gamma Function
  • Integrating a Function
  • Solving Matrices
  • Multiplying Polynomials
  • Finding Roots of a Function
  • Solving Differential Equations
  • Number Theory
  • Transforming Coordinates
  • Analytic Geometry
  • Solving Nonlinear Systems
  • Appendix
  • Index

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Cubic Splines with Known Derivatives

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If you know the second derivative at each of the data points, use the following procedure to run the Cubic Splines program.

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Starting the Program

To start the Cubic Splines program:

1. Select { INT } from the MATHEMATICS menu.
   The program displays:
   
2. Press { CUB }.
   The program displays:
   
3. Press { OLD }.

You can then begin entering the second derivative at each data point.

Entering the Derivatives

When you select { OLD } from the CUBIC SPLINES menu, the program displays:

1. Enter the number of data points and press { m }.
2. Press { EOD }.
   The program prompts you to enter the second derivative at each data point, beginning with the leftmost point.
   
3. Enter the derivative and press { ENT }.
4. Repeat step 3 until all the derivatives are entered.

The program then displays the menu shown below.

The Edit Menu

After you enter all the second derivatives, the program displays an EDIT? menu that allows you to change any of the values.

• If you do not want to edit any values, press { NO } and go to the section on interpolating.
• If you want to edit a value, press { YES }, and use the procedure in the section below.

Editing the Derivatives

When you select { YES } from the EDIT? menu, the program displays the same menu that you used to enter the second derivatives.

• To display the first derivative, press the [ CE ] key.
• To accept the current value and proceed to the next derivative, press { ENT }.
• To edit the current value, enter the correct value and press { ENT }.

When you press { ENT } to accept or edit the value of the last ( rightmost ) derivative, the program returns to the EDIT? menu. Selecting { NO } from that menu lets you interpolate.

Interpolating

When you select { NO } from the EDIT? menu, the program displays:

To interpolate:

1. Enter a value for x and press { x }.
   The program displays a corresponding value of y, such as:
   
2. Repeat step 1 for any other values of x.

Exiting the Program

When you are finished interpolating and are ready to exit the program:

1. Press { ESC }.
   The program displays the following menu. (This menu is normally used for "Cubic Splines with Known Data Points")
   
2. Press { ESC } to return to the CUBIC SPLINES menu.

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