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