Cantwell B.J. Introduction to symmetry analysis

Cambridge University Press, 2002. — 661 p. — (Cambridge Texts in Applied Mathematics). — ISBN-13 978-0-521-77183-2.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.Historical Preface
Introduction to Symmetry
Dimensional Analysis
Systems of ODEs and First-Order PDEs; State-Space Analysis
Classical Dynamics
Introduction to One-Parameter Lie Groups
First-Order Ordinary Differential Equations
Differential Functions and Notation
Ordinary Differential Equations
Partial Differential Equations
Laminar Boundary Layers
Incompressible Flow
Compressible Flow
Similarity Rules for Turbulent Shear Flows
Lie–B¨acklund Transformations
Variational Symmetries and Conservation Laws
B¨acklund Transformations and Nonlocal Groups
Appendixes
Review of Calculus and the Theory of Contact
Invariance of the Contact Conditions under Lie Point Transformation Groups
Infinite-Order Structure of Lie–B¨acklund Transformations
Symmetry Analysis Software