Maple Documentation

Maple V Release 3: A Brief Introduction

Maple on the Macintosh
The first step to starting Maple on the Mac is to get logged on. This is done by following the instructions that are posted on the south wall of the Math Lab (above the Mac SE/30s) or by following the instructions below. If you are already familiar with login procedures, skip to Section 2.

Section 1
Using the mouse, click and hold on the APPLE symbol (top-left corner) and drag it down to "Chooser". Release the mouse button and you will see the screen split into two halves. Click on the icon "AppleShare" in the upper-left corner. A new menu will appear on the right side. Click on the item "Math and Stat Aufs" and then click on the "OK" button. You will then be prompted to enter your username and password. The "Tab" button on the keyboard will allow you to toggle between your name and your password. Click on OK and you will be given a short list. The word "Applications" will be highlighted. Holding down the shift key, move the mouse to the Mac item below applications and click on it. Both items should now be highlighted. Click on OK. Two new icons should appear on the right side of your screen. (applications and mac)

Section 2
1. Use the mouse and double-click on the icon that says "Applications".
2. In the upper-left corner of this folder will be the item "MapleV R3". Double-click on this icon.
3. You will now be in the Maple folder. To start Maple, simply double-click on the icon that looks like a leaf and says "Maple"

Maple on the PC
1. The first step to starting Maple on the PC is to get logged in. This is simply a matter of typing in your username and then your password as prompted.
2. Press 'n' when asked about the University of Arizona Calculus Package.
3. At the N:\MSDOS> prompt, type "win" to start Windows. 4. Double-click on the "MapleV R3 for Windows" icon.

What is Maple?
Maple is a mathematical manipulation language. It has been designed to allow symbolic, numerical, and graphical computations. Some areas include: calculus, linear algebra, solving of equations, polynomials and common transformations, geometry, combinatorics, graph theory and number theory. Maple also includes its own complete programming language which has a syntax similar to FORTRAN, Pascal and C. Let us first consider symbolic manipulation. By allowing variables to remain unknown throughout a calculation we achieve greater accuracy since only the final solution is evaluated numerically. This follows since numerical approximations by nature are less accurate than exact solutions. Another benefit is the elimination of roundoff and truncation errors. As an example of symbolic computation, consider the following indefinite integral


First we can set a function f to be the equation
> f:=1/(exp(x)+1);

and then integrate f with respect to x.
>int(f,x);

>For a definite integral over the range 0 to 5, we would use
>int(f,x=0..5);

Maple solves problems numerically for the cases where a symbolic solution either does not exist or is too slow as well as for problems that are numerical in nature. Maple allows infinite precision (to the limit of computation power and your boredom level). Let us evaluate our previous expression to 25 decimal places.
> evalf(",25);

Had we simply typed "evalf("); we would have seen only ten decimal places. (The default setting for the evalf function). There are two interesting things to note here. Whenever we want to perform an operation on the last line of output (shown in red), we can type
> function(");
where function can be "eval", "diff", "int", "value", etc. The other point of note is that all functions that you wish to be executed must be followed by a semi-colon and be entered with the ENTER key. The RETURN key is not sufficient.

Basic Graphing Techniques
Functions with one or two unknowns can be represented graphically. This also holds true for parametric equations. these graphs can be depicted in a wide manner and variety of ways. One such graph in one such method is shown below.
> f := (x-sin(x^2));

We have defined our function, now we wish to plot it on the x-y axis between x = -3 and x = 3.
>plot(f,x=-3..3);
We will then be shown a graph similar to what follows.

Had we wanted to do a more complex plot, like a 3-D plot, we would have had to invoke the command:
> with(plots);
(List of functions omitted due to length.)
Using the "with(---)" command provides the user with a list of advanced features on a given topic. Another such example would be
>with(linalg);
for linear algebra functions.

Worksheet Environment
Worksheets in Maple are composed of four elements:

1. Input/Command: On the colour monitors these appear as blue letters followed by a semi-colon. Select input by clicking the Input box on the status bar.
2. Text: Select text by clicking the Text box on the status bar. Text allows you to add comments to you code. Text appears as black Times Roman font.
3. Output: Displays the results of Maple computations on a separate line in red Times Roman font.
4. Graphics: Graphics are displayed in a separate window from the main worksheet called a plot window. Graphics can be cut from the plot window and pasted in your worksheet or another application.

Basic Syntax of Commands
All command statements end with either a semi-colon or colon. If you have forgotten it and already hit Return, don't worry, simply insert it on the next line or go back using the cursor and place one at the end of your line. A common error that most new user's commit is to forget the line terminator and retype the command in a second time. (like below) Maple returns a syntax error in this case because it allows commands to span multiple lines.
> abs(-4)
> abs(-4);
syntax error:
abs(-4);
^
The caret ( ^ ) indicates where Maple first thinks there is an error. In the example above, Maple would have interpreted the command as "abs(-4)abs(-4);"
Another type of error sometimes seen is one in which the statement is syntactically correct but there is a different problem. Maple will output an error message depending on the error to help you correct the mistake.

A Sample Maple Session:

Consider the following matrix below:
> C:=matrix([[1,0,1],[2,2,1],[6,3,0]]);

Enter the following vector
>b:=[1,3,2];

Solving Ax=b, or in this case Cx=b, is a simple one line statement
> linsolve(C,b);
with x1, x2, and x3 respectively being

Finding the inverse of a given matrix is as easy as typing inverse, i.e.
>inverse(C);

Calculation of eigenvalues, characteristic equation and eigenvectors can also be simply calculated thus
> eigenvals(C);

> charpoly(C,lambda);

A common calculation in elementary linear algebra is Gaussian elimination. Note the following example
>gausselim(C);

It is also quite easy to get a reduced row echelon or Gauss-Jordan form of a matrix. Several intermediate steps will be shown that will help illustrate the method
> H:=extend(C,0,3,0);

> for i to 3 do H[i,i+3] := 1 od:eval(H);

>J:=gaussjord(H);

abs(x);

Absolute Value of x.

assume(x, prop);

Make assumption about x. (Will be displayed as x~).

diff(f,x);

Differentiate function f with respect to x.

eigenvals(A);

Find the eigenvalues of matrix A.

eval(A);

Evaluate A(number, matrix, etc.) at present time.

evalf(A,x);

Evaluate A at a floating point to x decimal places.

exp(x);

The exponent of x or e^x.

expand(expr);

Expand a polynomial or other expression.

factor (expr);

Factor a polynomial expression.

int(f,x);

Indefinite integral of f with respect to x.

int(f,x=a..b);

Definite integral of f over the range x=a to x=b.

limit(f,x=a);

The limit of function f in x as x approaches a.

inverse(A);

Find inverse of matrix A.

plot(f,x=a..b);

Plot function f dependent on variable x between a and b.

Rootof(expr);

Find the root(s) of an expression.

simplify(expr);

Simplify an expression.

sqrt(x);

Square root of x.

value(A);

Show value of A at present time.

with(name);

Access higher-order functions associated with name.

This list is by no means complete. If you are having difficulty with your syntax or are unable to locate a function, the help available on Maple is very well organized. In addition to this, there are two "Tours" available for Maple. To run "Quick Tour", instead of double-clicking on the "Maple" icon to start, click on and drag the "Quick Tour" icon onto the "Maple" icon. You can do the same for the "QTour Eng Sci" to start it.

This documentation does not cover the programming capabilities of Maple. If this is what you are interested in, an Australian University supplies a good Maple tutorial. You can access it by clicking HERE