Symmetries and Differential Equations

1. Front Matter

   Pages i-xiii

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2. Introduction

   • George W. Bluman, Sukeyuki Kumei

   Pages 1-3

3. Dimensional Analysis, Modelling, and Invariance

   • George W. Bluman, Sukeyuki Kumei

   Pages 4-30

4. Lie Groups of Transformations and Infinitesimal Transformations

   • George W. Bluman, Sukeyuki Kumei

   Pages 31-89

5. Ordinary Differential Equations

   • George W. Bluman, Sukeyuki Kumei

   Pages 90-162

6. Partial Differential Equations

   • George W. Bluman, Sukeyuki Kumei

   Pages 163-251

7. Noether’s Theorem and Lie-Bäcklund Symmetries

   • George W. Bluman, Sukeyuki Kumei

   Pages 252-301

8. Construction of Mappings Relating Differential Equations

   • George W. Bluman, Sukeyuki Kumei

   Pages 302-351

9. Potential Symmetries

   • George W. Bluman, Sukeyuki Kumei

   Pages 352-383

10. Back Matter

    Pages 384-413

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A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.

• calculus
• differential equation
• differential equations
• lie groups
• ordinary differential equation
• partial differential equation
• symmetry methods

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)

• Department of Mathematics, University of British Columbia, Vancouver, Canada

  George W. Bluman

• Faculty of Textile Science and Technology, Shinshu University, Ueda, Nagano 386, Japan

  Sukeyuki Kumei

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