FUNEX.TXT Function Experimenter Version 1.16, US 1994 INTRODUCTION: FUNCTION EXPERIMENTER is a program that can draw a curve of any mathematical function of the form y = f(x). The program can also be used as a calculator and to solve equations with one or two unknowns. The program is especially designed for teaching purposes, but can also be used for other purposes. FUNCTION EXPERIMENTER is so simple and user friendly that most pupils can use it with a minimum of instruction. Everywhere in the program are Help facilities that tell the user what to do. Error messages are instructive and easy to understand. SYSTEM REQUIREMENTS: This program requires Microsoft Windows version 3.0 or later. VGA color monitor and mouse recommended. Math coprocessor supported but not required. The program is quite fast even without a math coprocessor. INSTALLATION: There are no special considerations to take when installing this program. It is recommended that you make a directory named C:\FUNEX on your hard disk and copy all files from the program diskette or zip file to this directory. Use File Manager to do this. You probably want your Program Manager to have an icon for FUNCTION EXPERIMENTER. Select "New... " in the "File" menu of the Program Manager to make a new program item. The command line is FUNEX and the working directory is C:\FUNEX If you are in doubt, read the Windows manual. An alternative way to put the new icon into the Program Manager is to drag FUNEX.EXE with the mouse from File Manager into the appropriate group in Program Manager. This requires that both the File Manager and Program Manager are visible at the same time. (It is also possible to start the program from DOS by writing WIN C:\FUNEX\FUNEX ) TO THE TEACHER: The basic pedagogical idea behind the program is that it en- courages the pupil to experiment in a creative and intelligent way. If the pupil wants to know what happens when the formula is changed in a certain way, he or she can get the answer right away. A clever experiment is rewarded immediately with an interesting curve. The program can handle virtually any mathematical expression. No matter how fanciful an equation the pupil comes up with, the program will always give a correct answer. All standard mathematical functions are recognized, and the program is tolerant to different ways of writing. How to make a curve: The program has two long writing fields where you can write one or more equations with y on the left side of an equal sign and any expression containing x on the right side of the equal sign. Simply press Enter to see the curve whenever you have written an equation. It is recommended to let the pupils start with one of the examples that are stored in advance. This is done simply by clicking with the mouse on one of the buttons on the screen. This gives the pupils an example on how to write an equation, and thereby saving a lot of explanations. The pupils can now make changes in the equation they have got. They can start with changing the coefficients and see how this affects the shape of the curve. Later they can change a polynomial of second degree to one of a higher degree. They can swap x and y to see the curve get mirrored in the x=y line. Or you can leave it all to the pupils' fantasies to invent new functions. It is a good idea to make some buttons in advance with examples of the equations you want the pupils to work with. You can define a maximum of eight buttons. This is how to make your own buttons: First write the equation and make sure the curve is as you want it. It is recommended to use letters as coefficients and define the values of these on the second line. This makes it easier to change the coefficients. Write the equation neatly with spaces between the signs. You may adjust the limits of the coordinate system with the menu point "Axes". Use the same coordinate system for all equations. Now you can make a button for your equation by choosing the menu "Define" and "Buttons". When you are finished making buttons, save these as a setup file. Choose the menu "File" and "Save setup". The setup will be saved in a file with the name you choose. Choose the name STANDARD if you want the new setup to be loaded auto- matically next time the program is started. If you choose another name, then the pupil has to retrieve the setup by using the menu "File" and "Read setup". How to copy a setup from one PC to another: The setup files all have the extension FUN added to their names, and are stored in the directory C:\FUNEX. You can copy these files via a diskette to all the computers in the classroom. You may use the File Manager to copy files. How to prevent the pupils from changing the setup: You can prevent the standard setup file STANDARD.FUN or any other setup file from being changed by giving it the "Read Only" attribute. Open File Manager; pick the file you want to protect; choose the menu "File" and "Properties"; and check the "Read Only" attribute. Obviously, you have to remove the "Read Only" attribute again when you later want to change the setup. How to change the font: If you aren't satisfied with the style of the characters in the writing fields then you may change it. Use the program NOTEPAD to edit the file STANDARD.FUN. Write the name of the character font you want in the second line between the quotation marks, for example "Arial", "MS Sans Serif", or "Fixedsys". Loading the font may take a few seconds the first time you write an equation. If you are in doubt about how to use FUNCTION EXPERIMENTER, then use the help facilities. There are Help buttons every- where in the program telling you what to do. INTERNATIONAL USE: To define comma or point as decimals separator use the menu "Define" and "Decimals". You can use "*", "·", or "×" as multiplication sign. The asterisk "*" is recommended because it is readily available on the keyboard and is commonly used as multiplication sign in other computer programs. The dot "·" and cross "×" are allowed in order to support official standards. However, there is a risk that the dot will be confused with a point, and the cross will inevitably be confused with the letter X! You can use "/", ":", or "÷" as division sign. The american division sign "÷" should not be used in countries where this sign can be interpreted as a minus. A caret "^" is used as a sign for "raise to the power of". Using superscripts for this purpose, as is common standard outside the computer world, is not supported here because such an expression would be very complicated to write and difficult to read, especially if the exponent is a compound expression. If the abovementioned signs are not found on your keyboard, they may be written in the following way in FUNCTION EXPERIMENTER: Multiplication dot "·" = Alt+. Multiplication cross "×" = Alt+x American division sign "÷" = Alt+/ Caret "^" = Shift+6 or Alt+UpArrow National letters like ä, ã, â, å, etc. are allowed as symbols. The program does not distinguish between upper and lower case. USER FEEDBACK: Suggestions for improvement of this program from the users will be appreciated, and the most useful suggestions will be rewarded with a free update. If the program doesn't behave as expected, if the wording of help and error messages could be more clear, or if certain features are missing, then please write to the address below (no later than 1996). Please state whether you are using the program for teaching or for other purposes. You may include authentic unedited log-files showing the pupils' reactions. Please acknowledge that the basic concept of FUNCTION EXPERIMENTER is a program that is so logical and simple that a schoolkid can use it without instructions. I am not going to make 3-D drawing, import and export of data files, and other complicated features conflicting with this concept. There are other programs such as spreadsheets, math packages, and presentation programs to support such needs. SPECIFICATIONS: Internal accuracy: Approx. 15 significant digits. Numbers range: Real numbers from ± 10^(-308) to ± 10^308, and 0. Arithmetic operations: Addition, subtraction, multiplication, division, raising to power. Standard hierarchy of operators. Mathematic functions: Square root, round, magnitude, common and natural logarithms and exponential functions, trigonometric functions, inverse trigonometric functions, hyper- bolic functions, etc. All functions can be combined to expressions of virtually unlimited complexity. Results format: Fixed number of decimals or floating point with specified number of signifi- cant digits. Choice of point or comma as decimals separator. Exponential notation. 0/0, 0^0, imaginary and complex results indicated as "not defined". Division by 0 and overflow indicated as "infinity", or "- infinity". Graphic resolution: Depends on screen type. Every curve is drawn on basis of approx. 160 calculated points. Number of curves: Up to approx. 40 simultaneous curves in 9 colors. Printout: Printout of curve and equation on any printer or plotter supported by Windows. (Only version 2 of Function Experimenter) ORDERING INFORMATION: Version 1 of FUNCTION EXPERIMENTER is shareware and may be copied freely. Registered users will receive version 2 or later which has added facilities for printing curves. The registration fee is 50 US $ for single users and 200 $ for institutions, or equivalent amounts in other currencies. Methods of payment: - International checks. - Cash (registered mail). - Bank transfer to GiroBank Denmark, Swift code GICODKKK, Account No. 114 0817. - Europe: Giro transfer to Denmark 114 0817. No credit cards, please. ACON ApS Software P.O. Box 843 2400 Copenhagen NV DENMARK