# Category : Science and Education

Archive : CALC-1.ZIP

Filename : README.DOC

Dept. of Math.

University of IL.

Urbana, IL 61801.

Welcome to Calculus and Differential Equations V 9.

===================================================

This disk contains programs to help college students in

Math, Engineering, or Science. Some of them are already used in

the Differential Equations classes in U. of Illinois. More likely,

you would not have is a printer drive for EGA screen, (We used a

program named "EGAEPSON.COM included in commercial program "MATLAB")

and a plotter (we used IBM COLOR PLOTTER). But even without these

only if you have EGA SCREEN (and preferably 8087), you'll find these

interesting.

This disk is a shareware (suggested registration fee is $ 30.00)

and for those who register I will send a diskett with latest and

customized versions for their particular request (if possible),

and some more document files.

*** All these require EGA (640x350, 16 Color).

*** They are both stack and heap intensive. (Large Memory maybe

necessary I tested them only on 640 K machine. For speed, I

supressed stack-check option at compilation, except for Euler3d.)

They will work best, at fresh boot-up, when the stack is

almost free.

Tips On Use

===========

0. These are so user friendly that most of the time you may need

help for Math, not for usage of these programs.

1. DE.COM is for Differential Equations, and CALCULUS.COM is for

Calculus. They are compiled in Turbo Pascal (TURBO.COM).

Although they are not as fast as STRING.EXE and EULER.EXE, they

will be very convenient to use as an "Integrated Software", in

relatively small size.

***************************************************************

Warning: In DE.COM and CALCULUS.COM, when you enter new

functions, DON'T use SPACES. And use multiple * instead of

power (like x*x rather than x^2). You don't have to do this

for the other .exe programs.

****************************************************************

When you are in the program you want (like in ODE of DE.COM),

just press ENTER several times to see the default setting.

During the animation, press ESC to quit.

Explore on your own, and if you have problems, let me know.

2. ODE.EXE:

This is an update of my previous program "EULER.EXE".

It allows the user to choose between Runge-Kutta method

and Euler's Method to get the solutions.

This draws some solutions to the system of linear ODE

dx/dt = F1(x,y), dy/dt = F2(x,y), for selected initial

points.

Functions to Try:

F1 = x+y,

F2 = x-y,

F1 = y,

F2 = -x-y,

F1 = y,

F2 = -sin(x),

F1 = y,

F2 = .5*(1-x^2)*y-x.

The default is for Runge-Kutta with step size 0.2.

To switch to Euler, it would be reasonable to reduce

the step size (down to 0.003, for example). You will

be surprised to see how accurate the Runge-Kutta method is.

3. EULER3D.EXE is a test program for 3-dim extension of ODE.EXE.

It is very similar to ODE.EXE. But, careful in choosing

functions, (they are more capricious in 3-D). You can

choose xy-view or yz-view or zx-view or oblique view

from view menu. The colors represent z-values. Try to

change window and initial conditions (try very small z

value like -10), without changing the function first.

The function set up as a default is nice. You can try

F1 = 0.1, F2 = -z, F3 = y, (Circular Helix) or any of the

examples in 3. above as F2 and F3, letting F1 = constant

for interesting results.

4. STRING.EXE

First, press ENTER a couple of times to see the demo.

Any time, press ENTER to interrupt the animation. Try to change

parameters. Make sure (vertical step size)*(number of steps) <= 1.

This is well known stability criterion. Try to violate it and see

the unstable case (well, don't carry on that too far, in fear of

overflow).

Initial Functions to try:

cos(25*x)-1.

sin(50*x).

Use abs() to use functions with vertices.

(Maximum length of function expression < 60.)

In this update, you can enter the initial velocity.

5. LP.EXE uses 3-dim graphics window to show graphical meaning of

simplex method for linear programming. This is a sample version

and the full interactive version is in progress.

Acknowledgements

================

I must say I owe lots of ideas from the Mathematical environment

of U. of IL.

More specifically, LP.EXE is an outcome of the Computer Geometry

course by Professor G. Francis, in which he suggested the need and

relevance of such a program. Also, we had a well-known program

"LINPROG.COM" by Professor Muller, who gave me advices, and his

program helped me to understand this subject.

Also, we already had a string vibration program written by Professor

Dornhoff using Fourier Series Method, which fascinated me so much that

I began to explore the possibility for interactive program. So, I

first developed a parser (which should be optimized, because it

usually goes into a loop), and as Professor G. Francis suggested,

tried to use Numerical Method, for speed. And, it worked fine (of

course there was hard work behind this program).

The Euler programs use well-known Euler method. We had a version

written in BASICA (new functions possible but was slow and we could

not print EGA Screen in BASICA). So, I used my parser which is very

optimized (compare it with my old parsers used in DE.COM and

CALCULUS.COM I guess this is more than five times faster, although

those were faster than the BASICA version), and developed a version

in Microsoft C Version 5.01.

ADVERTISEMENT.

=============

I have another disk in PC-SIG:

Disk1070: Particle Simulation.

Also, another disk is under screening process in PC-SIG:

Vibrating, Rotating, and Cooling Surfaces.

Also, I submitted a Microsoft Windows programs in Differential

Equations in WISC-WARE.

In addition to these, I have lots of Mathematical Graphics

programs either for IBM PC, or for Silicon Graphics Machines,

mostly on the theme of Differential Equations and Differential

Geometry (most of them contain my optimized parser for highest

level of interactive environment). Registered users will get

informations on further developments.

*** As of version 9, I implemented a Boolean function '&':

Value & Limit = 1, if Value > Limit,

0, otherwise.

With this '&', you can enter functions with vertices or with

several components of different formula.

For example, in STRING.EXE,

try x&.2 - 2*(x&.5) + x&.8 to use a function like

____

___ ___

0 ____

0 .2 .5 .8 1

Have fun!

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This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

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