Introduction to Maple

In symbolic computation on computers, also known as computer algebra, keyboard and display replace the traditional pencil and paper in doing mathematical computations. Interactive computer programs, which are called computer algebra systems, allow their users to compute not only with numbers, but also with symbols, formulae, equations, and so on. Many mathematical computations such as differentiation, integration, and series expansion of functions, and inversion of matrices with symbolic entries, can be carried out quickly, with emphasis on exactness of results, and without much human effort. Computer algebra systems are powerful tools for mathematicians, physicists, chemists, engineers, technicians, psychologists, sociologists, … , in short, for anybody who needs to do mathematical computations. Com­ puter algebra systems are indispensable in modern pure and applied scien­ tific research and education. This book is a gentle introduction to one of the modern computer algebra systems, viz., Maple. Primary emphasis is on learning what can be done with Maple and how it can be used to solve (applied) mathematical problems. To this end, the book contains many examples and exercises, both elementary and more sophisticated. They stimulate you to use Maple and encourage you to find your way through the system. An advice: read this book in conjunction with the Maple system, try the examples, make variations of them, and try to solve the exercises.

The first two editions of this book have been very well received by the com­ munity, but so many revisions ofthe Maple system have occurred since then that simply reprinting the out-of-stock book would not do anymore. A ma­ jor revision of the book was inevitable, too. The wording "major revision" must be taken seriously because I not only corrected typographical errors, rephrased text fragments, and updated many examples, but I also rewrote complete chapters and added new material. In particular, the chapter on differential equations now discusses Liesymmetry methods, partial differen­ tial equations, and numerical methods. Linear algebra is based throughout the book on the packages LinearAlgebra and VectorCalculus, which re­ place the deprecated package linalg. Maple users are strongly advised to do their work with the new packages. The chapter on simplification has been updated and expanded; it discusses the use of assumptions in more detail now. Last, but not least, a new chapter on Grabner basis theory and the Groebner package in Maple has been added to the book. It includes many applications of Grabner basis theory. Many of the Maple sessions have been rewritten so that they comply with the most recent version of Maple. As a result of all this work, hardly any section in the book has been left untouched. vi Preface to the Third Edition From the Preface of the Second Edition The first edition ofthis book has been very wellreceived by the community.

MAPLE is a computer algebra system which, thanks to an extensive library of sophisticated functions, enables both numerical and formal computations to be performed. Until recently, such systems were only available to professional users with access to mainframe computers, but the rapid improvement in the performance of personal computers (speed, memory) now makes them accessible to the majority of users.

This tutorial shows how to use Maple both as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding tasks. It covers topics such as the basic data types and statements in the Maple language.

What's in this book This book contains an accelerated introduction to Maple, a computer alge­ bra language. It is intended for scientific programmers who have experience with other computer languages such as C, FORTRAN, or Pascal. If you wish a longer and more leisurely introduction to Maple, see (8, 27, 39). This book is also intended as a reference summary for people who use Maple infrequently enough so that they forget key commands. Chapter 4 is a keyword summary. This will be useful if you have forgotten the exact Maple command for what you want. This chapter is best accessed through the table of contents, since it is organized by subject matter. The mathematical prerequisites are calculus, linear algebra, and some differential equations. A course in numerical analysis will also help. Any extra mathematics needed will be developed in the book. This book was prepared using Maple V Release 3, although most of the examples will work with, at most, only slight modification in Maple V Release 2. This book does not require any particular hardware. The systems I have used in developing the book are machines running IBM DOS and WIN/OS2, Unix machines in an ASCII terminal mode, and x­ windows systems. There should be no adjustments necessary for readers equipped with Macintoshes or other hardware. Maple is an evolving system. New features will be described in the documentation for updates (?updates in Maple).