Introduction to Symmetry Analysis

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This text offers a broad, self-contained, introduction to the basic concepts of symmetry analysis and is intended primarily for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. The software requires Mathematica 2.2 or higher. MathReader 4.0 is included to permit the user without access to Mathematica to read the sample notebooks and follow the procedure used to find symmetries.

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Editorial Reviews

From the Publisher
'… an easy to read informal introduction to symmetry methods for ordinary and partial differential equations.' Monatshefte für Mathematik

'Overall, this was an enjoyable book to read, which I could recommend to someone to tackle as background reading. … if one's interest is in the application of symmetry analysis to problems arising in fluids, then this book discusses 'how' in detail.' Peter Clarkson, University of Kent

From The Critics
This graduate textbook introduces the methods of symmetry analysis based on Lie groups and how to express the symmetry properties of ordinary and partial differential equations. Sample applications in heat conduction, fluid mechanics, and nonlinear wave propagation are provided. The included CD-ROM contains Mathematica functions for finding the invariant groups of a differential equation and 60 sample notebooks. Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9780521777407
  • Publisher: Cambridge University Press
  • Publication date: 9/28/2002
  • Series: Cambridge Texts in Applied Mathematics Series , #29
  • Edition description: BK&CD-ROM
  • Pages: 654
  • Product dimensions: 6.97 (w) x 9.96 (h) x 1.34 (d)

Table of Contents

Preface; 1. Introduction to symmetry; 2. Dimensional analysis; 3. Systems of ODE's, first order PDE's, state-space analysis; 4. Classical dynamics; 5. Introduction to one-parameter Lie groups; 6. First order ordinary differential equations; 7. Differential functions and notation; 8. Ordinary differential equations; 9. Partial differential equations; 10. Laminar boundary layers; 11. Incompressible flow; 12. Compressible flow; 13. Similarity rules for turbulent shear flows; 14. Lie-Bäcklund transformations; 15. Invariance condition for integrals, variational symmetries; 16. Bäcklund transformations and non-local groups; Appendix 1. Review of calculus and the theory of contact; Appendix 2. Invariance of the contact conditions under Lie point transformation groups; Appendix 3. Infinite-order structure of Lie-Bäcklund transformations; Appendix 4. Symmetry analysis software.

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