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GraphDQ (c) Copyright (C) 1994 John E> Perry, /// Table of Contents I. General Information II. Graph Window III. Animating IV. Tools Window V. Printing VI. Palette Window VII. Equation Window VIII. Scale Window IX. Run-Time Help X. Quitting Time XI. Troubleshooting XII. Acknowledgements, etc. General Info GraphDQ is a program which graphs and demonstrates the flow of 2-dimensional differential equations. You define two differential equations, x' and y', in terms of x and y, then click anywhere on the graph window, and your Amiga will generate the graph of the equation. You can change the scale of the graph for both x and y axes, translate the graph to different points for further investigation, print out the graph, change the colors of the flow to suit your tastes, and generally have a good time exploring the fascinating world of Differential Equations. This program was developed while I was taking a class in graduate school at Northern Arizona University in Nonlinear Differential Equations. I needed something to check my work, and my Amiga, Sara, being such a wonderfully intuitive machine, seemed to fit the bill. All it would take was a few hours' work. ...famous last words, yes? So I spent the next few months developing this program for fun, and became more and more engrossed in it, until I decided I wanted to release it as a study aid for other students. Hope you enjoy it! GraphDQ probably requires 1 Meg of RAM; in fact, I'm certain of it. It also requires AmigaDOS2.0 or above. LEGAL STUFF NO WARRANTY OF ANY KIND IS IMPLIED OR GIVEN. YOU USE THE SOFTWARE INCLUDED AT YOUR OWN RISK. IF YOU HAVE TROUBLE WITH THE SOFTWARE, FEEL FREE TO CONTACT ME AT ONE OF THE ADDRESSES BELOW AND I WILL DO MY BEST TO HELP YOU (because I like the program and I like you for caring :) BUT YOU CANNOT HOLD ME RESPONSIBLE FOR ANY DAMAGE INCURRED TO YOUR COMPUTER SYSTEM, OTHER SOFTWARE, YOUR PERSONAL RELATIONSHIPS, OR YOUR SANITY THROUGH USE OF THIS PRODUCT. THIS PRODUCT HAS BEEN TESTED ON AN AMIGA 500 MICROCOMPUTER WITH A GVP A530 TURBO, RUNNING UNDER AMIGADOS 2.1. I HAVE TESTED THIS SOFWARE AS THOROUGHLY AS I HAVE BEEN ABLE TO DO DURING SEVERAL MONTHS' DEVELOPMENT. THIS PROGRAM IS COPYRIGHT (C) 1994 JOHN E. PERRY, III. THIS PROGRAM IS iNOTui IN THE PUBLIC DOMAIN BUT IS FREELY DISTRIBUTABLE. IF YOU LIKE THIS PROGRAM AND USE IT FREQUENTLY, PLEASE SEND ME EITHER A CARD OR A SMALL DONATION ($10 US) TO HELP DEFRAY THE COST OF FURTHER DEVELOPMENT.THOSE PEOPLE WHO DONATE OR SEND A CARD WILL BE NOTIFIED OF THESE ENHANCEMENTS AND WILL BE GIVEN FREE (shipping excluded) UPGRADES. I can be reached at any one of the addresses below: John E> Perry, /// TEMPORARY Northern Arizona University Box #6220 Flagstaff, Arizona 86011 PERMANENT 124 Archer Road Newport News, VA 23606-1102 INTERNET jep@nauvax.ucc.nau.edu Graph Window The Graph Window is the centerpiece of GraphDQ. It lies at the back of the screen, and has a pair of axes on it. In order to simplify the program and keep the graph uncluttered, the axes have no labels and no marked scale (however, that information is only a click away). Naturally, up is positive y and right is positive x. You can graph the currently defined equations by clicking the mouse buttons anywhere on the graph window. Clicking the left mouse button moves you forward in time; clicking the right button moves you backwards. The computer will graph forever unless: a) you hit a mouse button or press a key, or b) the graph runs off the screen, or c) it gets close enough to a previously-drawn trajectory to make the two trajectories indistinguishable. When the computer has stopped graphing, it animates the flow temporarily. (You can determine the flow colors in the Palette Window.) If you want to examine the flow, you can simply click on an existing trajectory and the computer will animate it for you. To exit GraphDQ, either press a key while the screen pointer looks like a cross-hair or use the Quit Button. Tools Window The Tools Window sits in the front of your screen, waiting for you to do something with it. It provides access to the following functions: Printing the graph Changing the flow colors Changing the differential equations Changing the scale or origin Run-Time Help Quitting If you'd like, you can see a diagram of the Tools Window by viewing the IFF file below: ToolsWindow.iff Printing Clicking on the Printer button will print the graph for you. In order to do this, your Amiga setup must satisfy the following requirements: a> you must have a printer capable of graphics output (obviously :) b> you need to make an assignment for TOOLS: which contains the GraphicDump command supplied by Commodore with the AmigaDOS operating system. This is almost always in the SYS:Tools/ drawer, so most people should just have to execute the command: "assign TOOLS: SYS:Tools/" Once you click on the button, a few seconds will pass before printing begins. The screen will turn a very light color and the Tools Window will disappear. This is to be expected! When the printout is done, the screen will return to normal. The standard printout has a grey field in the background of the graph. I have found that this makes the graph somewhat more soothing. If you prefer a black and white graph, disable the "Grey Field on Print?" check box gadget in the Palette Window. Palette Window The Palette window allows you to change the flow colors. It is a semi- standard window with slider gadgets to adjust the palette for the six flow colors. You have probably used something like this before if you've done much with your Amiga. When you are done, or if you've changed your mind, you can press either the check gadget in the lower left or the cross-out gadget in the lower right. The default flow colors are shades of grey. I've found that experimenting can produce really nice results. Being able to see the flow is a powerful tool in the study of differential equations, so this is a nice feature (if you don't mind my tooting my horn :). The top row of boxes allow you to select which color you want to change. Notice that, when animating, the lead flow color is the one on the left, the next flow color is the one to the right of that, and so on. The three slider gadgets allow you to change, from top to bottom, the red value of the color, the green value of the color, and the blue value of the color. Naturally, they only affect the color in the box currently selected (like most of the gadgets, selected means "looks pressed in"). In the lower center of the window is a check box gadget labeled "Grey Field on Print?" This determines whether you have a grey background when you print out your graph. If you prefer a black and white graph, disable this feature. (It is disabled when there is no check in the box.) Equation Window The Equation Window allows you to change the differential equations x' and y'. It presents you with two string prompts, a check gadget and a cross-out gadget. The two string prompts are for the two different differential equations: x' and y'. In the equations, you may use the variables "x" or "y", specifiy a constant number (e.g.: -2.256), or use one of the functions defined below. You should note the following: a> Precedence rules operate as in standard mathematics: unary operators are highest (exponents, functions like sine, cosine, etc.), followed by multiplication and division, followed by addition and subtraction. b> The interpreter does NOT have very strong error checking! While it ishouldui recover from most errors (though the graph may look peculiar), it may simply stop running if you make a mistake! Be careful and you should never have this problem, but you may. If it idoesui happen, reset your Amiga and try again. If you are certain you are having trouble with the program, reach me at one of the addresses listed in General Info and I will attend to the matter right away. c> Naturally, there are the standard big four: +, -, *, /. There is also the ^ function, indicating exponentiation. You may also use any of the following functions: sin sine cos cosine tan tangent asin arcsine acos arccosine atan arctangent ln natural logarithm log common logarithm exp exponential (e^whatever) Some examples: x^2 + 4*x + 4 asin (x * 2) 3 + x^2 -y + x * (x^2 + y^2 - 1)^2 -4y + 2 * x * y - 8 Please note that the interpreter will not understand if you leave out the multiplication sign, as is common in mathematics (2x, 2sinx, 2(x + y)). You must be careful not to do this! If the interpreter stumbles on this, it won't halt the program, but simply confuse you because the answer will be wrong. Scale Window The Scale window allos you to zoom in on any point of interest in your graph. It contains four string gadgets which request the scale and new origin. It contains check gadget and a cross-out gadget. The top two string gadgets request the new scale. The "scale" is the length of the positive axis; for example; an x scale of 10.0 means your graph window will graph x values from -10.0 to +10.0. The lower two string gadgets request the new origin. This means the program want to know where the center of the graph window is on the x-y plane. The default is (0,0), just as in regular Cartesian graphs. You can specify any number you like. Animating Animating is accomplished in one of two ways. The program always animates the flow briefly after drawing a new trajectory. If you don't want to draw a new trajectory but would still like to see the flow, you can click on an existing trajectory and GraphDQ will animate the flow. Run-Time Help GraphDQ offers a modicum of run-time help, though nothing as comprehensive or fancy as this guide. This is accessed by pressing the button in the Tools Window that looks like a question mark. Quitting There are two ways to quite the program (not that you'd want to :). The first is to press a key while the pointer looks like a cross-hair. The second is to click on the quitting gadget, located in the Tools Window. The Check and Cross Gadgets You will see the check and cross gadgets on several windows in this program. I call them this because that is what they look like: one is a check, the other a cross. Clicking on the check indicates that "Yes, I like what I've done; accept the changes (if any) and let's get back to work", while clicking on the cross indicates that "Ouch- I really don't like this! Cancel all changes!" Troubleshooting You should not have too much trouble with this program if you follow the directions. If you do and none of the suggestions below help, contact the author at the address given inGeneral Info (GenInfo. GraphDQ won't start. GraphDQ should run on any Amiga running AmigaDOS2.0 or higher, except possibly 512k machines. Try to free up some memory. GraphDQ crashes the computer while it's graphing. Increase the stack allocated to GraphDQ. You can do this by changing the preset value on the icon. GraphDQ won't print. Make sure you've assigned a TOOLS: drawer wherein Commodore's GraphicDump is located. If you want to use a different screen dump program, you will need to make an alias or rename it to GraphicDump. GraphDQ won't graph my equation correctly. Make sure you're using standard mathematical notation as described in the Equation Window section. If it's still not working right, contact the author (me). Maybe, even, there's not enough memory; close some other application and try GraphDQ again. GraphDQ won't graph my equation at iallui and stops responding. This shouldn't happen. <gulp!> Make sure your equation is legal; probably there's a typo. In either case, contact me and tell me what equation you're trying to graph. Perhaps there isn't enough memory; close some other application and try GraphDQ again. Acknowledgements My Lord and Savior Jesus Christ, for having created me with ability and willingness to work. Armadillo Software, for their Benchmark Modula-2 compiler.. Niklaus Wirth, for Modula-2. P.D. Terry, for one of the best books on teaching one how to program: An Introduction to Programming with Modula-2, published by Addison-Wesley. Commodore-Amiga, Inc., for the Amiga and AmigaGuide. Let's hope things look up for the wonderful Amiga community! Dr. Lawrence Perko, at Northern Arizona University, for the Differential Equations class, and for his book. I learned a great deal from both, typos and all... :) For those who are interested, the book is called Differential Equations and Dynamical Systems. Get the 2nd or, if available, the 3rd edition. Springer-Verlag publishes it. Dr. Vanessa Job, at Marymount University, for teaching me to think and use my head. And last, but not least, my parents, for starting it all with a TRS-80 Color Computer. Way back when 16K was hot stuff and 64K was what dreams were made of...