Symmetry and Integration Methods for Differential Equations

This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.

From the reviews of the second edition:

"The book by Bluman and Anco is an introduction to symmetry-based methods ... . The book is written in a clear and straightforward style, using many excellent worked examples ... . As someone who teaches an undergraduate course on symmetry methods, I would recommend Bluman and Anco’s book as a good source of examples and supplementary reading. ... for anyone wishing to master techniques for obtaining first integrals of ODEs, this book is outstanding." (Peter Hydon, UK Nonlinear News, June, 2003)

"The book under review devoted to symmetry and integration methods for differential equations is a significant update ... . The book has a Preface and Introduction well presenting its aim. ... Moreover, it has a final section Discussion which puts its contents into perspective by summarizing major results, by referring to related works and by introducing related material. ... the book should be particularly suitable for applied mathematicians, physicists and engineers. ... the publication of the present book should be highly welcome." (J. Synnatzschke, Zeitschrift für Analysis und ihre Anwendungen, Vol. 22 (1), 2003)