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

• Main Author: Seiler, Werner M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Algorithms and Computation in Mathematics, 24
• Subjects: Mathematics.; Algebra > Data processing.; Algebra.; Differential Equations.; Differential equations, partial.; Partial Differential Equations.; Ordinary Differential Equations.; Commutative Rings and Algebras.; Theoretical, Mathematical and Computational Physics.; Symbolic and Algebraic Manipulation.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-01287-7
• Physical Description: XXII, 650 p. online resource.
• ISBN: 9783642012877
• ISSN: 1431-1550

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