Involution The Formal Theory of Differential Equations and its Applications in Computer Algebra
Werner M. Seiler (Author)
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 Gröbner 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
eBook, English, 2010
1st ed. 2010 View all formats and editions
Springer Berlin Heidelberg : Imprint: Springer, Berlin, Heidelberg, 2010
1 online resource (662 p.).
9781282835184, 9783642012877, 9783642012884, 9786612835186, 1282835181, 3642012876, 3642012884, 6612835184
1126504161
Formal Geometry of Differential Equations
Involution I: Algebraic Theory
Completion to Involution
Structure Analysis of Polynomial Modules
Involution II: Homological Theory
Involution III: Differential Theory
The Size of the Formal Solution Space
Existence and Uniqueness of Solutions
Linear Differential Equations
Miscellaneous
Algebra
Differential Geometry
Description based upon print version of record
English