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Computer Algebra Recipes: An Advanced Guide to Scientific Modeling

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A computer algebra system (CAS) not only has the number \crunching" and plotting capability of traditional computing languages such as Fortran and C, but also allows one to perform the symbolic manipulations and derivations required in most mathematically based science and engineering courses. To introduce students in these disciplines to CAS-based mathematical modeling and computation, the authors have previously developed and classroom tested the text Computer Algebra Recipes: A Gourmet's Guide to the Mathematical Models of Science [EM01] based on the Maple CAS. Judging by course evaluations and reader feedback, the response to this book and the computer algebra approach to modeling has been very favorable. With the release of several new versions of Maple since this text was published and the authors' accumulation of many insightful comments and helpful suggestions, a second up-dated edition seemed expedient. However, incorporating all the changes would make an already lengthy book even longer. So the topics of the Gourmet's Guide have been reorganized into two new stand-alone volumes, an already-published Introductory Guide [EM06] and this Advanced Guide.

In this book, we explore mathematical models involving linear and nonlinear ordinary and partial di®erential equations (ODEs and PDEs). This volume, which may be used either as a course text or for self-study, features an eclectic collection of Maple computer algebra worksheets, or \recipes," that are systematically organized to illustrate graphical, analytical, and numerical techniques applied to ODE/PDE-based scienti¯c modeling. No prior knowledge of Maple is assumed, the early recipes introducing the reader to the basic Maple syntax, the subsequent recipes introducing further Maple commands and structure on a need-to-know basis.
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