Symmetries and Differential Equations

George W. Bluman, Sukeyuki Kumei (auth.)9780387986548, 0387986545

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.

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Table of contents :
Front Matter….Pages i-xiii
Introduction….Pages 1-3
Dimensional Analysis, Modelling, and Invariance….Pages 4-30
Lie Groups of Transformations and Infinitesimal Transformations….Pages 31-89
Ordinary Differential Equations….Pages 90-162
Partial Differential Equations….Pages 163-251
Noether’s Theorem and Lie-Bäcklund Symmetries….Pages 252-301
Construction of Mappings Relating Differential Equations….Pages 302-351
Potential Symmetries….Pages 352-383
Back Matter….Pages 384-413