Algebraic Theory of Differential Equations by Malcolm A. H. MacCallumAlgebraic Theory of Differential Equations by Malcolm A. H. MacCallum

Algebraic Theory of Differential Equations

EditorMalcolm A. H. MacCallum, Alexander V. Mikhailov

Paperback | January 5, 2009

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Integration of differential equations is a central problem in mathematics and several approaches have been developed by studying analytic, algebraic, and algorithmic aspects of the subject. One of these is Differential Galois Theory, developed by Kolchin and his school, and another originates from the Soliton Theory and Inverse Spectral Transform method, which was born in the works of Kruskal, Zabusky, Gardner, Green and Miura. Many other approaches have also been developed, but there has so far been no intersection between them. This unique introduction to the subject finally brings them together, with the aim of initiating interaction and collaboration between these various mathematical communities. The collection includes a LMS Invited Lecture Course by Michael F. Singer, together with some shorter lecture courses and review articles, all based upon a mini-program held at the International Centre for Mathematical Sciences (ICMS) in Edinburgh.
Title:Algebraic Theory of Differential EquationsFormat:PaperbackDimensions:248 pages, 8.98 × 5.98 × 0.51 inPublished:January 5, 2009Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521720087

ISBN - 13:9780521720083


Table of Contents

Preface; 1. Galois theory of linear differential equations Michael F. Singer; 2. Solving in closed form Felix Ulmer and Jacques-Arthur Weil; 3. Factorization of linear systems Sergey P. Tsarev; 4. Introduction to D-modules Anton Leykin; 5. Symbolic representation and classification of integrable systems A. V. Mikhailov, V. S. Novikov and Jing Ping Wang; 6. Searching for integrable (P)DEs Jarmo Hietarinta; 7. Around differential Galois theory Anand Pillay.

Editorial Reviews

"... A useful book that serves as an introduction to both the Galois theory of (linear) differential equations and several other algebraic approaches to such equations. Libraries will definitely want to have a copy."
Fernando Q. Gouvea, MAA Reviews