Library Services | Technical University of Kenya

Your cart is empty.
Normal view MARC view ISBD view

Involution [electronic resource] : The Formal Theory of Differential Equations and its Applications in Computer Algebra / by Werner M. Seiler.

By: Seiler, Werner M [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Algorithms and Computation in Mathematics: 24Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Description: XXII, 650 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642012877.Subject(s): Mathematics | Algebra -- Data processing | Algebra | Differential Equations | Differential equations, partial | Mathematics | Partial Differential Equations | Ordinary Differential Equations | Commutative Rings and Algebras | Algebra | Theoretical, Mathematical and Computational Physics | Symbolic and Algebraic ManipulationDDC classification: 515.353 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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 theory. Special emphasis is put on a constructive approach leading to effective algorithms.
Tags from this library: No tags from this library for this title. Log in to add tags.
No physical items for this record

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.

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 theory. Special emphasis is put on a constructive approach leading to effective algorithms.

There are no comments for this item.

Log in to your account to post a comment.

2017 | The Technical University of Kenya Library | +254(020) 2219929, 3341639, 3343672 | library@tukenya.ac.ke | Haile Selassie Avenue