CALCULUS.ENG File
                                     
                            Exploring Calculus
                              by Dennis York
                                     
               Copyright (c) Hewlett-Packard Company, 1992.


Overview
--------

The Exploring Calculus application provides a number of functional
extensions to the HP 48, wrapped in a soft key interface.  The application
is designed to aid students in the exploration of calculus and pre-calculus
mathematics.

The programs were inspired by Dr. Bert Waits and are more fully documented
in "The Graphing Calculator and Computer Graphing Laboratory Manual";
Demana, Waits, Vonder Embse, & Foley; Addison-Wesley Publishing Company;
Third Edition.


Procedure
---------

After transferring the CALCULUS directory object to your HP 48 using binary
transfer mode:

Press the [VAR] key.  Press the |CALCU| soft key to enter the sub
directory. Press the |KEYS| soft key (you might have to press [NXT] to find
it.  You will see the top line of the menu structure below in the soft
keys.

In the following paragraphs, the symbol {S} equals the HP 48 Integral Sign.

NWEX    FUNC    GRPH     {S}    DFEQ    IR
          |       |       |       |
          |       |       |     NWXY    ->XMN   ->XMX   ->STP   ->X Y   KEYS
          |       |       |     EULR    IEULR   RUNK    PLOT    TABLE   KEYS
          |       |       |     ERASE   ->YMN   ->YMX   ADFX            KEYS
          |       |       |
          |       |     ->A B   HP{S}   N->R{S} N->T{S} N->S{S} KEYS
          |       |
          |     ERASE   F(X)    F'(X)   A->{S}  ZMFIT   KEYS
          |     A->TA                   FSTR    BETR    KEYS
          |     ->XMN   ->XMX   ->YMN   ->YMX           KEYS
          |
        X->F    X->F'   ->H     X->NF'  KEYS

The soft keys are defined as follows:

|NWEX|    NeW EXpression: allows you to key in a new expression or edit the
          current one.  It automatically defines the function as F, its
          symbolic derivative as DF, and sets a number of system variables
          so that they are correct for learning mathematics.

|FUNC|    FUNCtion evaluation: Allows the function and its derivative to be
          evaluated interactively.
          
          |X->F|    Given X, computes F(X).
          
          |X->F'|   Given X, computes the derivative from DF(X) which is
                    the analytic solution.
          
          |->H|      Stores the delta value H for the numerical derivative.
          
          |X->NF'|  Given X computes the numerical derivative of F(X).
          
          |    |     Blank key.
          
          |KEYS|    Goes back to top level menu.

|GRPH|    GRaPHing: Allows functions, derivatives, and  integrals to be
          graphed interactively.
          
          |ERASE|   Erases current graph (done automatically when limits
                    are changed).
          
          |F(X)|    Plots F(X).
          
          |F'(X)|   Plots F'(X).
          
          |A->{S}|  Plots integral of F(T) with limits of A to X.
          
          |ZMFIT|   Sets the Y plotting limits to the limits of the last
                    function plotted.
          
          |KEYS|    Goes back to top level menu.

[NXT]     To see the next six soft keys.
          
          |A->TA|   Draws a line tangent to F(X) at point A and puts the
                    equation of the resulting line in the stack.
          
          |   |      Blank key.
          
          |   |      Blank key.
          
          |FSTR|    Makes plotting faster.
          
          |BETR|    Increases plotting resolution.
          
          |KEYS|    Goes back to top level menu.

[NXT]     To see the NeXT six soft keys.
          
          |->XMN|    Sets the minimum limit of X.
          
          |->XMX|    Sets the maximum limit of X.
          
          |->YMN|    Sets the minimum limit of Y.
          
          |->YMX|    Sets the maximum limit of Y.
          
          |    |     Blank key.
          
          |KEYS|    Goes back to top level menu.

|{S}|     Integration: Allows different methods of integration to be
          compared.
          
          |->A B|    Stores the limits of integration.
          
          |HP{S}|   Computes integral using the HP 48's built-in
                    capability.
          
          |N->R{S}| Computes integral using rectangular elements.
          
          |N->T{S}| Computes integral using trapezoidal elements.
          
          |N->S{S}| Computes integral using Simpson's Rule.
          
          |KEYS|    Goes back to top level menu.

|DFEQ|    Differential Equations: Allows different numerical methods of
          solution to differential equations to be compared.
          
          |NWXY|    Automates definition of G(X,Y).
          
          |->XMN|    Sets the minimum limit of X.
          
          |->XMX|    Sets the maximum limit of X.
          
          |->STP|    Sets the step size H.
          
          |->X Y|    Sets the initial conditions X0 and Y0.
          
          |KEYS|    Goes back to top level menu.

[NXT]     To see the NeXT six soft keys.
          
          |EULR|    Saves Euler solution in {Sigma}DAT.
          
          |IEULR|   Saves improved Euler solution in {Sigma}DAT.
          
          |RUNK|    Saves Runge-Kutta solution in {Sigma}DAT.
          
          |PLOT|    Plots points from most recent solution above.
          
          |TABLE|   Moves to statistics menu to view the data in tabular
                    form.
          
          |KEYS|    Goes back to top level menu.

[NXT]     To see the NeXT six soft keys.
          
          |ERASE|   Clears the graph.
          
          |->YMN|    Sets Ymin for plotting.
          
          |->YMX|    Sets Ymax for plotting.
          
          |   |      Blank key.
          
          |ADFX|    Uses an analytic function F(X) to add a third column to
                    {Sigma}DAT for comparison.
          
          |KEYS|    Goes back to top level menu.

| IR |     Infrared Output: Clones the application to another HP 48.

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V 1.0 04/26/92 03:24 PM