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[资源] 【分享】Computer Algebra Recipes.Springer.2006

Computer Algebra Recipes: An Introductory Guide to the Mathematical Models of Science
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Authors(Editors):
Richard H. Enns
George C. McGuire
Publisher:Springer
Pub Date: 2006
Pages:435
ISBN-10 0-387-25767-5 e-ISBN 0-387-31262-5
ISBN-13 978-387-25767-9

Preface
A computer algebra system (CAS) not only has the ability to "crunch numbers"
and plot results, like traditional computing languages such as Fortran and C,
but it can also perform the symbolic manipulations and analytic derivations
required in most undergraduate and graduate science and engineering courses.
To introduce students in these disciplines to mathematical modeling and computation
using a CAS, the authors have previously published Computer Algebra
Recipes: A Gourmet ^s Guide to the Mathematical Models of Science, based on
the Maple CAS. Judging by course evaluations and reader feedback, the response
to this book and the CAS approach has been quite favorable. After
observing students' enthusiasm, their higher quality of work, their ability to
solve more realistic problems, and best of all, their ability to answer "what
if?" questions, we believe that the importance of using a CAS in learning and
exploring mathematically based science subjects cannot be overstated.
With the release of new, more powerful, versions of the Maple CAS since the
first edition was published and the accumulation of many insightful comments
and helpful suggestions from readers of the text, it seemed timely to produce a
second edition. However, incorporating the necessary changes and suggestions
would make an already lengthy book even longer, so the topics of the first
edition have been reorganized and expanded into two new standalone volumes
based on the expected mathematical level of the reader.
In this first volume, we assume the reader's familiarity with linear algebra,
vectors, and elementary calculus, and knowledge of (but not necessarily expertise
at) linear ordinary diflPerential equations. The second volume {Computer
Algebra Recipes: An Advanced Guide to the Mathematical Models of Science)
deals with more advanced differential equation models, both ordinary and partial,
and nonlinear as well as linear.
Each 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"
drawn from a wide variety of disciplines, including biology, economics, medicine,
engineering, game theory, physics, mathematics, and chemistry. These recipes
are systematically organized to illustrate graphical, analytical, and numerical
techniques applied to scientific modeling. No prior knowledge of Maple is assumed
in either volume, the early recipes of each book introducing the reader to
the basic Maple syntax, and the subsequent recipes introducing further Maple
commands and structure on a need-to-know basis.
The recipes are fully annotated in the text and typically presented as "stories"
or in a historical context. Each recipe takes the reader from the analytic
formulation or statement of an interesting mathematical model to its analytic
or numerical solution, and to a graphical visualization of the answer where relevant.
The graphical representations vary from static 2-dimensional pictures,
to contour and vector field plots, to 3-dimensional graphs that can be rotated,
and to animations of analytic and numerical solutions.
Every recipe is followed by a set of problems that readers can use to check
their understanding or develop the topic further. For your convenience in solving
these problems and to facilitate further exploration of a given topic, the
unannotated recipes for each volume are included on an accompanying CD.

本资源13.7 MB。

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Computer Algebra Recipes_An Introductory Guide to the Mathematical Models of Science.Richard H. Enns.Springer.2006

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