Maple V

The design and implementation of the Maple system is an on-going project of the Symbolic Com putation Group at the University of Waterloo in Ontario, Canada. This manual corresponds with version V (roman numeral five) of the Maple system. The on-line help subsystem can be invoked from within a Maple session to view documentation on specific topics. In particular, the command ?updates points the user to documentation updates for each new version of Maple. The Maple project was first conceived in the autumn of 1980, growing out of discussions on the state of symbolic computation at the University of Waterloo. The authors wish to acknowledge many fruitful discussions with colleagues at the University of Waterloo, particularly Morven Gen tleman, Michael Malcolm, and Frank Tompa. It was recognized in these discussions that none ofthe locaIly-available systems for symbolic computation provided the facilities that should be expected for symbolic computation in modern computing environments. We concluded that since the basic design decisions for the then-current symbolic systems such as ALTRAN, CAMAL, REDUCE, and MACSYMA were based on 1960's computing technology, it would be wise to design a new system "from scratch". Thus we could take advantage of the software engineering technology which had become available in recent years, as well as drawing from the lessons of experience. Maple's basic features (elementary data structures, Input/output, arithmetic with numbers, and elementary simplification) are coded in a systems programming language for efficiency.

Learn how to use the modern techniques offered by Maple V, a powerful and popular computer algebra system. The Maple V Primer: Release 4 covers all the basic topics a reader needs to know to use Maple V in its major revision encompassed in Release 4 to do algebra and calculus, solve equations, graph 2- and 3-dimensional plots, perform simple programming tasks, and prepare mathematical documents. Every common command and function is supported by a specific example, so you won't waste time struggling with the syntax. Graphs, plots, and other Maple output are provided along with the syntax, so the user knows what to expect when she or he uses a particular command. And all the examples come with a short discussion, answering questions you might have about applying the example to your own work. This is a painless - even fun - way to learn how to use Maple V.

Maple V Mathematics Learning Guide is the fully revised introductory documentation for Maple V Release 5. It shows how to use Maple V as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding or specialized tasks. Topics include the basic data types and statements in the Maple V language. The book serves as a tutorial introduction and explains the difference between numeric computation and symbolic computation, illustrating how both are used in Maple V Release 5. Extensive "how-to" examples are presented throughout the text to show how common types of calculations can be easily expressed in Maple. Graphics examples are used to illustrate the way in which 2D and 3D graphics can aid in understanding the behaviour of problems.

Accompanying CD-ROM includes all Maple V input that appears in the book.

Differential Equations with Maple V provides an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Maple V is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Maple V can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are also provided. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

A complete software package consisting of the printed book and a CD-ROM (with diskettes available on request). The interactive text includes: * A graphical user interface for easy navigation through the text along with animations that explain linear algebra concepts geometrically. * Interactive lessons with emphasis on experimentation and conjecturing. * A collection of labs which strengthens the learning of the concepts. * Applications which stress modelling and the use of linear algebra in various disciplines. * A unique library of interactive "high-level" functions written in Maple V that can be used in different modes. * A stand alone testing system. The authors believe that students of mathematics should enjoy, understand, assimilate, and apply the skills and concepts they study, and, as such, here they play a fundamental and active role throughout the learning process.