Algebraic Theory of Differential Equations (London Mathematical Society Lecture Note Series, Series Number 357)

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-programme Held At The International Centre For Mathematical Sciences (icms) In Edinburgh. Edited By Malcolm A. H. Maccallum, Alexander V. Mikhailov. This Book Presents Lectures Given During A School And Workshop Organized At Heriot-watt University In July And August--preface. Includes Bibliographical References. "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." "These selected contributions reflect different approaches to the integration of differential equations, originating from Differential Galois Theory, Symmetry, Integrability and Soliton Theory. The ideas of several mathematical communities are here brought together and connections between them sought."--BOOK JACKET Cover; Title; Copyright; Contents; Preface; 1 Galois Theory of Linear Differential Equations; 1.1 Introduction; 1.2 What is a Linear Differential Equation?; 1.3 Basic Galois Theory and Applications; 1.4 Local Galois Theory; 1.5 Algorithms; 1.6 Inverse Problems; 1.7 Families of Linear Differential Equations; 1.8 Final Comments; Bibliography; 2 Solving in closed form; 2.1 Introduction; 2.1.1 Integrating via linear dierential equations; 2.1.2 Solutions of Linear Dierential Equations; 2.2 Linear differential equations versus linear differential systems; 2.2.1 Equivalent dierential systems A unique introduction to the subject, reflecting different approaches to the integration of differential equations