Symmetry Methods for Differential Equations: A Beginners Guide by Peter E. HydonSymmetry Methods for Differential Equations: A Beginners Guide by Peter E. Hydon

Symmetry Methods for Differential Equations: A Beginners Guide

byPeter E. Hydon

Paperback | January 28, 2000

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A good working knowledge of symmetry methods is very valuable for those working with mathematical models. This book is a straightforward introduction to the subject for applied mathematicians, physicists, and engineers. The informal presentation uses many worked examples to illustrate the major symmetry methods. Written at a level suitable for postgraduates and advanced undergraduates, the text will enable readers to master the main techniques quickly and easily. The book contains some methods not previously published in a text, including those methods for obtaining discrete symmetries and integrating factors.
Title:Symmetry Methods for Differential Equations: A Beginners GuideFormat:PaperbackDimensions:228 pages, 9.72 × 6.85 × 0.51 inPublished:January 28, 2000Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521497868

ISBN - 13:9780521497862


Table of Contents

1. Introduction to symmetries; 1.1. Symmetries of planar objects; 1.2. Symmetries of the simplest ODE; 1.3. The symmetry condition for first-order ODEs; 1.4. Lie symmetries solve first-order ODEs; 2. Lie symmetries of first order ODEs; 2.1. The action of Lie symmetries on the plane; 2.2. Canonical coordinates; 2.3. How to solve ODEs with Lie symmetries; 2.4. The linearized symmetry condition; 2.5. Symmetries and standard methods; 2.6. The infinitesimal generator; 3. How to find Lie point symmetries of ODEs; 3.1 The symmetry condition. 3.2. The determining equations for Lie point symmetries; 3.3. Linear ODEs; 3.4. Justification of the symmetry condition; 4. How to use a one-parameter Lie group; 4.1. Reduction of order using canonical coordinates; 4.2. Variational symmetries; 4.3. Invariant solutions; 5. Lie symmetries with several parameters; 5.1. Differential invariants and reduction of order; 5.2. The Lie algebra of point symmetry generators; 5.3. Stepwise integration of ODEs; 6. Solution of ODEs with multi-parameter Lie groups; 6.1 The basic method: exploiting solvability; 6.2. New symmetries obtained during reduction; 6.3. Integration of third-order ODEs with sl(2); 7. Techniques based on first integrals; 7.1. First integrals derived from symmetries; 7.2. Contact symmetries and dynamical symmetries; 7.3. Integrating factors; 7.4. Systems of ODEs; 8. How to obtain Lie point symmetries of PDEs; 8.1. Scalar PDEs with two dependent variables; 8.2. The linearized symmetry condition for general PDEs; 8.3. Finding symmetries by computer algebra; 9. Methods for obtaining exact solutions of PDEs; 9.1. Group-invariant solutions; 9.2. New solutions from known ones; 9.3. Nonclassical symmetries; 10. Classification of invariant solutions; 10.1. Equivalence of invariant solutions; 10.2. How to classify symmetry generators; 10.3. Optimal systems of invariant solutions; 11. Discrete symmetries; 11.1. Some uses of discrete symmetries; 11.2. How to obtain discrete symmetries from Lie symmetries; 11.3. Classification of discrete symmetries; 11.4. Examples.

From Our Editors

Mathematical models are important in understanding and further developing mathematical theories. In Symmetry Methods for Differential Equations: A Beginner’s Guide, Peter E. Hydon provides valuable information for people working with mathematical models. Readers will learn the main techniques of modelling in an easy-to-understand manner. The text focusses on methods for obtaining discrete symmetries and integrating factors, with a series of line diagrams to help readers understand the most difficult aspects of the text. This book is a great learning and reference guide for professionals and undergraduate students in mathematics, physics and engineering.

Editorial Reviews

"Throughout the text numerous examples are worked out in detail and the exercises have been well chosen. This is the most readable text on this material I have seen and I would recommend the book for self-study." Mathematical Reviews