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Catalogue Information
Field name	Details
Dewey Class	515.353
Title	Involution (EB) : The Formal Theory of Differential Equations and its Applications in Computer Algebra / by Werner M. Seiler.
Author	Seiler, Werner M.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2010.
Physical Details	XXII, 650 pages : online resource.
Series	Algorithms and computation in mathematics 1431-1550 ; ; 24
ISBN	9783642012877
Summary Note	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 GrÃ¶bner 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-Kähler theory. Special emphasis is put on a constructive approach leading to effective algorithms.:
Contents note	1 Introduction -- 2 Formal Geometry of Differential Equations -- 3 Involution I: Algebraic Theory -- 4 Completion to Involution -- 5 Structure Analysis of Polynomial Modules -- 6 Involution II: Homological Theory -- 7 Involution III: Differential Theory -- 8 The Size of the Formal Solution Space -- 9 Existence and Uniqueness of Solutions -- 10 Linear Differential Equations -- A Miscellaneous -- B Algebra -- C Differential Geometry -- References -- Glossary -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-01287-7
Links to Related Works	Subject References: Algebra . Commutative Rings and Algebras . Differential Equations . Differential equations, Partial . Ordinary differential equations . Partial differential equations . Symbolic and Algebraic Manipulation . Theoretical, Mathematical and Computational Physics . Authors: Seiler, Werner M. . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and computation in mathematics . Classification: 515.353 .

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

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