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© 2010

Involution

The Formal Theory of Differential Equations and its Applications in Computer Algebra

Book

Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 24)

Table of contents

  1. Front Matter
    Pages 1-18
  2. Werner M. Seiler
    Pages 1-8
  3. Werner M. Seiler
    Pages 9-61
  4. Werner M. Seiler
    Pages 63-104
  5. Werner M. Seiler
    Pages 105-165
  6. Werner M. Seiler
    Pages 167-234
  7. Werner M. Seiler
    Pages 235-262
  8. Werner M. Seiler
    Pages 263-327
  9. Werner M. Seiler
    Pages 329-355
  10. Werner M. Seiler
    Pages 357-429
  11. Werner M. Seiler
    Pages 431-507
  12. Werner M. Seiler
    Pages 509-528
  13. Werner M. Seiler
    Pages 529-584
  14. Werner M. Seiler
    Pages 585-616
  15. Back Matter
    Pages 1-34

About this book

Keywords

Gröbner bases algebra calculus formal theory of differential equations geometry integrability involution overdetermined systems

Authors and affiliations

  1. 1.FB 17 Mathematik und InformatikUniversität KasselKasselGermany

About the authors

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

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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)