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

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Springer Science & Business Media, 26 okt. 2009 - 650 pagina's
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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.

 

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Inhoudsopgave

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
10 Linear Differential Equations
431
A Miscellaneous
509
B Algebra
529
C Differential Geometry
585
References
617
Glossary
637
Index
639
Copyright

9 Existence and Uniqueness of Solutions
357

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Over de auteur (2009)

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.


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