Differential Equations With Symbolic Computation

Differential Equations With Symbolic Computation
~
Dongming Wang (Editor), Zhiming Zheng (Editor)

Editorial Reviews
Product Description
This book presents the state of the art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions. The 20 chapters are written by leading experts and are structured into three parts. The book is worth reading for researchers and students working on this interdisciplinary subject but may also serve as a valuable reference for everyone interested in differential equations, symbolic computation, and their interaction.
Product Details

* Hardcover: 374 pages
* Publisher: Birkhäuser Basel; 1 edition (September 27, 2005)
* Language: English
* ISBN-10: 3764373687
* ISBN-13: 978-3764373689

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Applications of Abstract Algebra with MAPLE

Applications of Abstract Algebra with MAPLE
~
Richard E. Klima, Neil Sigmon, and Ernest Stitzinger

Product Description
The mathematical concepts of abstract algebra may indeed be considered abstract, but its utility is quite concrete and continues to grow in importance. Unfortunately, the practical application of abstract algebra typically involves extensive and cumbersome calculations-often frustrating even the most dedicated attempts to appreciate and employ its intricacies. Now, however, sophisticated mathematical software packages help obviate the need for heavy number-crunching and make fields dependent on the algebra more interesting-and more accessible.Applications of Abstract Algebra with Maple opens the door to cryptography, coding, Polya counting theory, and the many other areas dependent on abstract algebra. The authors have carefully integrated Maple V throughout the text, enabling readers to see realistic examples of the topics discussed without struggling with the computations. But the book stands well on its own if the reader does not have access to the software.The text includes a first-chapter review of the mathematics required-groups, rings, and finite fields-and a Maple tutorial in the appendix along with detailed treatments of coding, cryptography, and Polya theory applications.Applications of Abstract Algebra with Maple packs a double punch for those interested in beginning-or advancing-careers related to the applications of abstract algebra. It not only provides an in-depth introduction to the fascinating, real-world problems to which the algebra applies, it offers readers the opportunity to gain experience in using one of the leading and most respected mathematical software packages available.

# Hardcover: 272 pages
# Publisher: CRC; 1 edition (September 28, 1999)
# Language: English
# ISBN-10: 0849381703
# ISBN-13: 978-0849381706

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Algorithms for computer algebra

Algorithms for computer algebra
~
Keith O. Geddes, Stephen R. Czapor, and George Labahn

eview
`The Computer Algebra community has been waiting for years for this book to appear. ...the book is a masterpiece and can be recommended to everyone interested in the algorithms for computer algebra, either as a reference for further research or just to give the casual user an idea why things work as good (or as bad) as they do in computer algebra packages. ...the recommendation would be clear: Buy this book! As it stands now my only advice is to stay away from this book, because you might be tempted to buy it anyway (at least I was).' Computer Algebra Nederland Newsletter, June 1993


Product Description
Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.
Product Details

* Hardcover: 608 pages
* Publisher: Springer; 1 edition (September 30, 1992)
* Language: English
* ISBN-10: 0792392590
* ISBN-13: 978-0792392590

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Computer Algebra Recipes for Mathematical Physics

Computer Algebra Recipes for Mathematical Physics
~
Enns R.H.

Product Description

Hundreds of novel and innovative computer algebra
Product Details

* Paperback: 390 pages
* Publisher: Birkhäuser Boston; 1 edition (December 1, 2004)
* Language: English
* ISBN-10: 0817632239
* ISBN-13: 978-0817632236

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Symbolic Integration I: Transcendental Functions (Algorithms and Computation in Mathematics)

Symbolic Integration I: Transcendental Functions (Algorithms and Computation in Mathematics)
~
Bronstein M.

Review

From the reviews of the second edition:

"It discusses … the integration of transcendental functions … . Indeed, one of the most remarkable characteristics of this book is that it requires from its readers very little beyond a basic knowledge of calculus and algebra. … This is an extremely well-written book on a beautiful topic that deserves to be better known to practising mathematicians and teachers of mathematics alike."

S. C. Coutinho, The Mathematical Gazette, Vol. 90 (5l9), 2006

"[...] The book contains many examples and exercises for the reader to get a feeling not only of the theoretical but also the practical aspects of the algorithms. It is designed as a textbook and well suited for courses about these constructive aspects of calculus. A "must have" for the bookshelf of every library."

H.-G.Gräbe, Zeitschrift für Angewandte Analysis und Ihre Anwendungen, Vol. 24, Issue 4, 2005

"The second edition of Bronstein's excellent book [...] contains a new chapter on parallel integration (also called the new Risch algorithm or the Risch-Norman
algorithm) [...] The first nine chapters of the book contain some improvements and a couple of additional exercises. Bronstein's book still presents the state of the art in the domain of integration of transcendental functions. Its unique blend of detailed mathematics and clear description of algorithms make it both a standard reference and a handbook for researchers and designers of computer algebra systems and a useful, easy to read textbook for teachers and students."

Friedrich Schwarz (Paderborn), Zentralblatt MATH 1059

From the reviews of the first edition:

"The goal of this well-written book is to present the state of the art in the domain of "integration in finite terms". ... Both aspects of the work, mathematics and implementation, are present in the book. Moreover, Bronstein has chosen a good level of detail, and in such a way that he only deals with the case of transcendental functions. ..."

J.M.Ollagnier, Mathematical Reviews 2002

"... It makes an excellent textbook for courses in computer algebra. It contains many exercises and the algorithms are presented in pseudocode, which is easy to implement in any computer algebra system. For those interested in symbolic integration it will become the standard reference."

N.A.van Arkel, Medelingen van het wiskundig genootschap 1998

"... The writing is excellent, and the author provides a clear and coherent treatment of the problem of symbolic integration of transcendental functions. Each chapter includes several worked examples and a list of additional exercises. Every researcher and teacher in symbolic computation should have access to this book."

F.Winkler, Computing Reviews 1997

"... In fact, this book is an excellent blend of mathematics and algorithms. ... This well-written book serves as a good foundation to the topic of symbolic integration. ... Highly recommendable."

P.Kravanja, Journal of Computational and Applied Mathematics / Newsletter on Computational and Applied Mathematics 1997

"My first thought on seeing this book was "I wish I had written it" - it resembles my lecture notes on the subject, but is better and more complete. ... In sum, the book does what it sets out to do, does it well, and should be on the bookshelf of every implementer or teacher. For the latter, the author indicates various ways through the material, depending on the aims and background of the course being taught."

J.Davenport, The SAC Newsletter 2, 1997

"Symbolic Integration I is the second edition of an extremely thorough account of the problem of integration in finite terms for transcendental functions. … This book was written by the world’s leading expert in the area. … it does what it sets out to do and does it extremely well." (Sam Blake, SIAM Review, Vol. 50 (1), 2008)


Product Description

Symbolic Integration I is destined to become the standard reference work in the field. Manuel Bronstein is a leading expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.

This second edition offers a new chapter on the Risch-Norman algorithm, a number of other improvements and a couple of additional exercises.

From the Reviews of the First Edition:
Product Details

* Hardcover: 325 pages
* Publisher: Springer; 2nd edition (December 14, 2004)
* Language: English
* ISBN-10: 3540214933
* ISBN-13: 978-3540214939

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Infinite Words, Volume 141: Automata, Semigroups, Logic and Games (Pure and Applied Mathematics)

Infinite Words, Volume 141: Automata, Semigroups, Logic and Games (Pure and Applied Mathematics)
~
Perrin D., Pin J.-E.

Editorial Reviews
Review
The most impressive aspect of the book "Infinite Words" by Dominique Perrin and Jean-Eric Pin is the extent of its coverage.
It is a virtually complete compendium of everything to do with infinite words: infinite-time automata; connections to semigroups, topology and logic; infinite games; bi-infinite words; infinite trees.
Before holding this book in my hand, I was not fully
conscious of the extent of the progress in this field in the last twenty years.
Robert McNaughton


Book Description
Being the very first comprehensive treatment of the theory of Infinite Words, this book is the reference for researchers and graduates in this field.

Product Details

* Hardcover: 550 pages
* Publisher: Academic Press; 1 edition (March 3, 2004)
* Language: English
* ISBN-10: 0125321112
* ISBN-13: 978-0125321112

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