Elementary Lie group analysis and ordinary differential equations. (English) Zbl 1047.34001

Ibragimov, Nail H.

Wiley Series in Mathematical Methods in Practice 4. Chichester: Wiley (ISBN 0-471-97430-7/hbk). xviii, 347 p. (1999).

From the preface: The present book provides students and teachers with an easy to follow and comprehensive introduction to differential equations and Lie group analysis with an emphasis on useful tools rather than on general theory. In fact, this is the first self-contained university text on ordinary differential equations after Sophus Lie’s classical lectures, where all the basic integration methods are derived from group-invariance principles. The text is designed to meet the needs of beginners and provides material for several undergraduate and postgraduate courses.

MSC:

34-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
22E70	Applications of Lie groups to the sciences; explicit representations
22-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups
34C14	Symmetries, invariants of ordinary differential equations

Keywords:

Lie group; ordinary differential equations