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 eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Algorithms and Computation in Mathematics, 24
• Subjects: Mathematics.; Computer science > Mathematics.; Algebra.; Commutative algebra.; Commutative rings.; Differential equations.; Partial differential equations.; Physics.; Partial Differential Equations.; Ordinary Differential Equations.; Commutative Rings and Algebras.; Theoretical, Mathematical and Computational Physics.; Symbolic and Algebraic Manipulation.

Table of 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.