Geometric Approaches to Differential Equations

A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.

Peter J. Vassiliou (Edited by), Ian G. Lisle (Edited by)

9780521775984, Cambridge University Press

Paperback, published 13 March 2000

238 pages, 22 b/w illus. 2 tables
22.9 x 15.2 x 1.4 cm, 0.36 kg

'It is a pleasure to report on this outstanding collection of articles … a coherent set of expository lecture notes prepared by leading experts in the geometric aspects of differential equations.' Australian Mathematical Society Gazette

This book provides a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The aim of the book is to present an overview of this developing subject and a brief introduction to a number of related topics, including twistor theory, vortex filament dynamics, calculus of variations, exterior differential systems and Bäcklund transformations. Written by leading experts, this book is an ideal starting point for graduate students embarking on research. It will also be of use to researchers and anybody wishing to learn more about this burgeoning field of mathematical endeavour.

Preface
1. Geometric approaches to differential equations: an introduction Peter J. Vassiliou
2. Bäcklund and his works: applications in soliton theory Colin Rogers, Wolfgang K. Schief and Mark E. Johnston
3. Recent developments in integrable curve dynamics Annalisa Calini
4. An elementary introduction to exterior differential systems Niky Kamran
5. Cartan structure of infinite Lie pseudogroups Ian G. Lisle and Gregory J. Reid
6. Cartan's method of equivalence David Hartley
7. The inverse problem in the calculus of variations and its ramifications Geoff E. Prince
8. Twistor theory Michael K. Murray.

Subject Areas: Calculus & mathematical analysis [PBK]