Maple

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple lan­ guage, and is written for all Maple users, regardless of their discipline or field(s) of interest. All the built-in mathematical, graphic, and system­ based commands available in Maple V Release 4 are detailed herein. Please note that The Maple Handbook does not teach the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together provide a basic overview of the capabil­ ities of Maple, it is highly recommended that you also read a more thorough tutorial such as Introduction to Maple by Andre Heck, or one of standard manuals shipped with Maple V Release 4. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of prob­ lems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different categories, e.g., calculus, algebra, data manipulation, etc.; the commands within a subset are ex­ plained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system.

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple language, and is written for all Maple users, regardless of their dis­ cipline or field(s) of interest. All the built-in mathematical, graphic, and system-based commands available in Maple V Release 2 are detailed herein. Please note that The Maple Handbook does not teach about the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together do provide a basic overview of the capabilities of Maple, it is highly recom­ mended that you also read a more thorough tutorial such as In­ troduction to Maple by Andre Heck or First Leaves: A Tutorial Introduction to Maple. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of problems) in a specific subject area.

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple lan­ guage, and is written for all Maple users, regardless of their discipline or field(s) of interest. All the built-in mathematical, graphic, and system­ based commands available in Maple V Release 4 are detailed herein. Please note that The Maple Handbook does not teach the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together provide a basic overview of the capabil­ ities of Maple, it is highly recommended that you also read a more thorough tutorial such as Introduction to Maple by Andre Heck, or one of standard manuals shipped with Maple V Release 4. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of prob­ lems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different categories, e.g., calculus, algebra, data manipulation, etc.; the commands within a subset are ex­ plained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system.

"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple."

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.

Buch und CD-ROM ermöglichen es, ohne Vorkenntnisse das Computeralgebra-System MAPLE zu nutzen, um elementare mathematische Probleme am Computer zu lösen. Sie liefern einen schnellen Zugriff auf die Lösung mit der Beschreibung der zugehörigen MAPLE-Befehle. Besondere Vorteile: Alle Probleme werden exemplarisch behandelt.

This "hands-on" book is for people who are interested in immediately putting Maple to work. The reader is provided with a compact, fast and surveyable guide that introduces them to the extensive capabilities of the software. The book is sufficient for standard use of Maple and will provide techniques for extending Maple for more specialized work. The author discusses the reliability of results systematically and presents ways of testing questionable results. The book allows a reader to become a user almost immediately and helps him/her to grow gradually to a broader and more proficient use. As a consequence, some subjects are dealt with in an introductory way early in the book, with references to a more detailed discussion later on.

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple language, and is written for all Maple users, regardless of their dis­ cipline or field(s) of interest. All the built-in mathematical, graphic, and system-based commands available in Maple V Release 2 are detailed herein. Please note that The Maple Handbook does not teach about the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together do provide a basic overview of the capabilities of Maple, it is highly recom­ mended that you also read a more thorough tutorial such as In­ troduction to Maple by Andre Heck or First Leaves: A Tutorial Introduction to Maple. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of problems) in a specific subject area.