# 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

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