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Maple for Windows

Bert G. Wachsmuth

In 1959 at MIT a group of researchers developed a system called MACSYMA, the first computer algebra system. That system was intended partially to convince the science community that computers could perform significant intellectual tasks. The system could manipulate symbols as well as numbers, and was useful for tasks for which computers could not be used before. Since then several other computer algebra systems were developed, with different underlying philosophies. Three such systems have proved especially useful: Mathematica, Maple, and Derive. Mathematica is the Cadilac of computer algebra systems: it is expensive, uses a lot of system resources, but delivers superb performance. Maple is the VW of computer algebra systems: it is affordable and sturdy, cheap on system resorces, delivers adequate performance, but lacks an aura of grandeur. Derive is the car for the non-driver: it has all the features of a real car, but it assists you in handling the controls whenever possible and in doing so may occasionally restrict your creativity to avoid mistakes.

To use Maple for Windows it helps to be familiar with Microsoft Windows. When you start Maple, you will see its main window on the screen and after a seconds Maple will be ready for your input. On top of the main window you will find a menu bar which offers several choices. You might want to see what each menu item has to offer before starting to use Maple. Three things should be kept in mind at all times:

Maple has an extremly good help facility, as well as a ‘Help Browser’:
 To get help on a particular topic, type help(keyword); to find a particular command, select Help | Browse
Every command in Maple must by typed in, according to some syntax rules. Use the help facilities to find out the exact form of each command and its options
Every command in Maple must end with a semicolon. If you forget to enter a semicolon, no computation will happen. However, you can simply type a semicolon on the next line by itself to start the computation

A Brief Maple Session

Start Maple and type the lines on the left. Maple should act in the way indicated. Remember, Maple is a Windows program so you can use the familiar window resizing commands, cut-and-paste, scrolling, etc.

 help(intro); Displays an introductory help message about Maple 123 - 5/2 * (44/7 - 99/2)^2; add fractions and numbers evalf(%); gives a float-point (decimal) approximation of last result. The single percent stand for the ‘last computed expression’ evalf(Pi,100); show decimal approximation of Pi to 100 decimals P := x -> x^2 - x - 6; defines a function P(x) P(sqrt(2)); evaluates P at root(2) factor(P(x)); factors P(x) over the rationals expand(%); expands a factored expression solve(P(x)=0,x); solve the equation P(x) = 0 for x plot(P(x),x=-5..5) plots polynomial for x in [-5,5] f := x -> x^3 - 2*x; defines a function f(x) plot({P(x),f(x)},x=-5..5); plots P(x) and f(x) in one coordinate system

Here is a short list of useful Maple functions. Use the help facility to find out more about each command.

Essential Commands

 diff find derivatives plot create a two-dimensional plot of an expression evalf evaluate an expression simplify simplify an expression int integrate expressions (definite /indefinite integral) solve solve an equation or system of equations limit calculate the limiting value of an expression subs substitute one expression into another % single percent stand for last computed expression %% double percent stand for second-to-last computed expression

More Commands

 assume make assumptions such a a variable being positive normal normalize a rational expression convert convert an expression to a different form numer extracts numerator of fraction denom extracts denominator of fraction rhs, lhs extract right-hand-side or left-hand-side of an equations expand simplify an expression by distribution law seq generates a sequence according to some rule factor factor a polynomial sum finds the sum of expressions fsolve find approximate solutions

Functions

 abs(x) absolute value exp(x), E^x exponential function sin(x), cos(x), tan(x) trig. Functions log(x), ln(x) natural logarithm sqrt(x) square root function arctan(x), arcsin(x), arccos(x) inverse trig. Functions

Constants

 Pi constant Pi = 3.1415 infinity positive infinity E or exp(1) exponential number e = 2.7182

Simple Programming

 defining simple functions `fname := x -> expression;` iterations ```for i from 1 by 2 to 10 do expression; od; ``` defining general functions ```fname := proc(x) expression1; expression2; ...; end; ``` conditional evaluation ```if condition1 then statement else statement fi; ```

There are several nice booklets available which explain Maple with a student's viewpoint in mind. One such booklet is usually provided when you purchase the Student Edition of Maple. Another very nice book is Maple V: First Leaves' by B.W. Char and others, Springer Verlag 1992.

 Some sample problems using Maple