Overview
- Ground-breaking monograph on the topic
- Includes supplementary material: sn.pub/extras
Part of the book series: Algorithms and Computation in Mathematics (AACIM, volume 24)
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Keywords
Table of contents (13 chapters)
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Front Matter
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Back Matter
Reviews
From the reviews:
“The first book that provides a self-contained treatment of constructive and algorithmic ideas and methods in FTDE … . the book Involution is unique, self-contained … complete and, in addition, well-written with numerous instructive examples and comprehensive bibliography devoted to the constructive differential-geometric and computer-algebraic aspects of involutivity analysis of differential and polynomial equations and their applications. It can be recommended to researchers, postgraduate and advanced graduate students.” (Vladimir P. Gerdt, Computeralgebra-Rundbrief, October, 2010)
“This book deals with the formal theory of general … systems of differential equations. … starts with an introduction to a geometric approach to differential equations via the jet bundle formalism. … this is a very interesting book with many instructive examples and strong emphasis placed on a constructive approach leading to effective algorithms. It is well written, so it is suitable for and recommended to anyone who is interested in computer-algebraic aspects of involutivity analysis of differential and polynomial equations and their applications.” (Lech Slawik, Mathematical Reviews, Issue 2011 h)
“The book targets the mathematically mature reader who can handle the frequent jumps between geometric and algebraic approaches. It is written at the postgraduate level … . Seiler strikes a good balance between theory, algorithms, and applications. … Seiler’s book hopes to bridge two research communities: one of differential geometers concerned with the formal analysis of differential equations, the other of (computer) algebraists interested in computations with polynomial modules.” (Willy Hereman, SIAM Review, Vol. 53 (3), 2011)
Authors and Affiliations
About the author
W.M. Seiler is professor for computational mathematics (algorithmic algebra) at Kassel University. His research fields include differential equations, commutative algebra and mechanics. He is particularly interested in combining geometric and algebraic approaches. For many years, he has been an external developer for the computer algebra system MuPAD.
Bibliographic Information
Book Title: Involution
Book Subtitle: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Authors: Werner M. Seiler
Series Title: Algorithms and Computation in Mathematics
DOI: https://doi.org/10.1007/978-3-642-01287-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Hardcover ISBN: 978-3-642-01286-0Published: 15 November 2009
Softcover ISBN: 978-3-642-26135-0Published: 14 March 2012
eBook ISBN: 978-3-642-01287-7Published: 26 October 2009
Series ISSN: 1431-1550
Edition Number: 1
Number of Pages: XXII, 650
Number of Illustrations: 39 b/w illustrations, 8 illustrations in colour
Topics: Partial Differential Equations, Ordinary Differential Equations, Commutative Rings and Algebras, Algebra, Theoretical, Mathematical and Computational Physics, Symbolic and Algebraic Manipulation