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

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...

Table of Contents:

• 1 Introduction
• 2 Formal Geometry of Differential Equations
• 3 Involution I: Algebraic Theory
• 4 Completion to Involution
• 5 Structure Analysis of Polynomial Modules
• 6 Involution II: Homological Theory
• 7 Involution III: Differential Theory
• 8 The Size of the Formal Solution Space
• 9 Existence and Uniqueness of Solutions
• 10 Linear Differential Equations
• A Miscellaneous
• B Algebra
• C Differential Geometry
• References
• Glossary
• Index.