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These programs visualize and solve high-level mathematical equations, conveniently graphing them for you on an EGA monitor. Great for students, scientists, or anyone who just enjoys math. The DIFFERENTIAL EQUATION program can solve a variety of both ordinary and partial differential equations. You can also integrate factors of an equation, and create a graph of power series solutions. Use the CALCULUS program to find the derivatives of an expression in x and/or y. Other features include graphing functions of y=f(x), graphing first and second derivatives, solving and graphing parametric equations, finding the integral of simple functions, and finding the surface contour of a function z=f(x,y). An MS-Windows version is available for registered users.
Disk No: 1072 Program Title: DIFFERENTIAL EQUATIONS and CALCULUS version 9 PC-SIG version 1.3 These programs visualize and solve high-level mathematical equations, conveniently graphing them for you on an EGA monitor. Great for students, scientists, or anyone who just enjoys math. The DIFFERENTIAL EQUATION program can solve a variety of both ordinary and partial differential equations. You can also integrate factors of an equation, and create a graph of power series solutions. Use the CALCULUS program to find the derivatives of an expression in x and/or y. Other features include graphing functions of y=f(x), graphing first and second derivatives, solving and graphing parametric equations, finding the integral of simple functions, and finding the surface contour of a function z=f(x,y). Usage: Differential Equations and Calculus. Special Requirements: EGA graphics (some programs need a 8087 math chip). How to Start: Type GO (press enter). Suggested Registration: $30.00 File Descriptions: CALCULUS COM CALCULUS program. DE COM DIFFERENTIAL EQUATIONS program. EULER3D EXE Test program for 3-D extension of ODE.EXE. LP EXE Uses 3-D graphics window to show graphical meaning of simplex method for linear programming. ODE EXE Subprogram README BAT Batch file to view README.DOC. README DOC Documentation file. STRING EXE Subprogram. PC-SIG 1030D E Duane Avenue Sunnyvale CA 94086 (408) 730-9291 (c) Copyright 1988 PC-SIG, Inc.
╔═════════════════════════════════════════════════════════════════════════╗ ║ <<<< Disk No 1072 DIFFERENTIAL EQUATIONS and CALCULUS >>>> ║ ╠═════════════════════════════════════════════════════════════════════════╣ ║ To start a program type, FILENAME (press enter), FILENAME is equal ║ ║ to the name of the program that you want to load. Example, if you ║ ║ wanted to load the EULER program you would type EULER (press enter). ║ ╚═════════════════════════════════════════════════════════════════════════╝
Byoung Keum, October 5, 1988 Dept. of Math. University of IL. Urbana, IL 61801. Welcome to Calculus and Differential Equations V 10. =================================================== 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 a printer driver 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 an EGA SCREEN (and preferably a math coprocessor), you'll find these programs 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. Also, I have Microsoft Windows versions for most of these programs. And smaller (and often much faster) versions of programs doing only one thing (like integration menu) are also available for registered users upon, request. *** 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. Professor Dornhoff's program used the Fourier Series method, for which it was necessary to compute beforehand and write to a file, because of the speed. For an interactive program with compilable language, one needs a parser (formula interpreter) and much faster algorithm. 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) in Microsoft C, V 5.1. The ODE programs use well-known Euler method, and 4-th order Runge- Kutta methods to show the graphical solution of linear system of Ordinary Differential Equations. In U. of IL., we had a version using Euler's method, written in BASICA (slow, but BASICA has a built-in parser!). I used my super-optimized parser (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 already 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!
Volume in drive A has no label Directory of A:\ CALCULUS COM 62572 9-26-88 1:16p DE COM 64928 6-28-88 10:26p EULER3D EXE 54760 8-11-88 11:25p FILE1072 TXT 1546 10-28-88 9:42a GO BAT 38 5-31-88 1:16p GO TXT 540 10-20-88 5:06p LP EXE 40294 6-07-88 1:54a ODE EXE 56486 8-15-88 1:01p README BAT 222 9-26-88 11:36p README DOC 9106 10-05-88 11:52p STRING EXE 53472 8-12-88 1:23a 11 file(s) 343964 bytes 11264 bytes free