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.
Introduction Dimensional Analysis, Modeling, and Invariance Lie Groups of Transformations and Infinitesimal Transformations Ordinary Differential Equations (ODEs) Partial Differential Equations (PDEs) References Author Index Subject Index
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)
Introduction * Dimensional Analysis, Modeling, and Invariance * Lie Groups of Transformations and Infinitesimal Transformations * Ordinary Differential Equations (ODEs) * Partial Differential Equations (PDEs) * References * Author Index * Subject Index
This book provides a comprehensive treatment of symmetry methods and dimensional analysis. The authors discuss aspects of Lie groups of point transformations, contact symmetries, and higher order symmetries that are essential for solving differential equations. Emphasis is given to an algorithmic, computational approach to finding integrating factors and first integrals. Numerous examples including ordinary differential equations arising in applied mathematics are used for illustration and exercise sets are included throughout the text. This book is designed for advanced undergraduate or beginning graduate students of mathematics and physics, as well as researchers in mathematics, physics, and engineering.
This book includes a comprehensive treatment of Lie groups of transformations and thorough discussions of basic symmetry methods for solving ordinary and partial differential equations. It is particulary suitable for physicists, applied mathematicians and engineers. In this second edition, the authors have added sections on contact transformations and Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order. References have also been updated.