Involution

The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas. It presents for the first time in book form the theory of Pommaret bases, a special kind of Grobner bases closely related to Koszul homology, and contains an extensive discussion of the existence and uniqueness of solutions of formally well-posed initial value problems and a novel presentation of Vessiot's dual version of the Cartan-Kahler theory. Special emphasis is put on a constructive approach leading to effective algorithms.

ISBN 3642012868   Volumes 1 ISBN13 9783642012860 (What's this?)   Weight (grammes) 1280 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG   Published in Berlin Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K   Series ISSN 24 Format Hardback   Series title Algorithms and Computation in Mathematics Publication date 14 Nov 2009   Height (mm) 235 DEWEY 515.35   Width (mm) 155 DEWEY edition DC22   Spine width (mm) 41 Pages 672   Academic level Professional / Scholarly

1		Introduction		1
2		Formal Geometry of Differential Equations		9
3		Involution I: Algebraic Theory		63
4		Completion to Involution		105
5		Structure Analysis of Polynomial Modules		167
6		Involution II: Homological Theory		235
7		Involution III: Differential Theory		263
8		The Size of the Formal Solution Space		329
9		Existence and Uniqueness of Solutions		357
10		Linear Differential Equations		431
A		Miscellaneous		509
B		Algebra		529
C		Differential Geometry		585
		References		617
		Glossary		637
		Index		639

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)

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