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# Lecture 13 Notes

These are the notes for lecture 13
Mark
--
Today's fortune:
A day for firm decisions!!!!! Or is it?

Title: **Math 481/581 Lecture 13: Maple & Mathematica**
# Math 481/581 Lecture 13: Maple & Mathematica

####
© 1998 by Mark Hays <hays@math.arizona.edu>. All rights reserved.

This document discusses the *basics* of Maple and
Mathematica.

# Introduction

Maple and mathematica are programs that are principally used
for doing symbolic mathematical calculations. If you want to
calculate the eigenvalues of a 4x4 matrix, get the roots
of a cubic polynomial, etc. then these are the programs for
you.
With suitable coaching, you can make these programs perform
fairly sophisticated analyses for you; however, you will
find that doing so often takes considerable skill.

The reason that this is the case is threefold. First, it is
fairly easy to come problems that you can do by hand that
these programs cannot do. Second, there exist problems for
which these programs actually return an *incorrect*
answer. Finally, there are "easy" problems for which you
know that there is a solution, but the program fails to
find it.

In other words, you have to be a little careful. Whenever
either of these programs gives you an answer, you should put
it to the test -- this may involve a bit of extra work, but it
could save you a lot of embarrasment. If the program returns
a "root" of a polynomial, you should plug the "root" back into
the polynomial and make sure that you get zero. Corresponding
techniques should be used for "integrals" of functions,
"solutions" of linear systems, and so on.

If you are interested in getting *numerical* solutions to
larger problems, you should probably have a look at something
like Matlab or IDL. These packages are optimized for numerical
operations (in terms of memory usage and speed), unlike the
symbolic packages. Also, the numerical packages tend to
document the numerical methods they employ. Symbolic packages
tend to "black box" such details; this is dangerous and evil.

# The Basics

The following "tutorials" were created as worksheets in
maple and mathematica. The content is more or less derived
from the mathematica tutorial on the SWIG page (see link
below). The latest versions of these programs have the
ability to save your worksheet as HTML --- this is how
the following documents were generated:

# Further Information

The online help for maple and mathematica is fairly
comprehensive. If you are already familiar with the
basics, the online help is probably sufficient as a
reference document.
If you are just getting started, you'll probably want to
buy one of the many books available on the subject. The ASUA
bookstore usually stocks copies of several of the most
popular books.

Additional online information on maple and mathematica is
available from the SWIG page:

http://www.math.arizona.edu/swig/onlinedocs.html