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

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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.


Author(s): Werner M. Seiler (auth.)
Series: Algorithms and Computation in Mathematics 24
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010

Language: English
Pages: 650
Tags: Partial Differential Equations;Ordinary Differential Equations;Commutative Rings and Algebras;Algebra;Theoretical, Mathematical and Computational Physics;Symbolic and Algebraic Manipulation

Front Matter....Pages 1-18
Introduction....Pages 1-8
Formal Geometry of Differential Equations....Pages 9-61
Involution I: Algebraic Theory....Pages 63-104
Completion to Involution....Pages 105-165
Structure Analysis of Polynomial Modules....Pages 167-234
Involution II: Homological Theory....Pages 235-262
Involution III: Differential Theory....Pages 263-327
The Size of the Formal Solution Space....Pages 329-355
Existence and Uniqueness of Solutions....Pages 357-429
Linear Differential Equations....Pages 431-507
Miscellaneous....Pages 509-528
Algebra....Pages 529-584
Differential Geometry....Pages 585-616
Back Matter....Pages 1-34