Baumann G. Symmetry Analysis of Diff Equ with Mathematica 2000

Textbook in PDF format

The study of symmetries of differential equations is an old subject. Thanks to Sophus Lie we today have available to us important information on the behavior of differential equations. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. They can provide conservation laws for differential equations. The theory presented here is based on Lie, containing improvements and generalizations made by later mathematicians who rediscovered and used Lie's work. The presentation of Lie's theory in connection with Mathematica is novel and vitalizes an old theory. The extensive symbolic calculations necessary under Lie's theory are supported by MathLie, a package written in Mathematica.
Introduction
Elements of Symmetry Analysis
Derivatives
Symmetries of Ordinary Differential Equations
Point Symmetries of Partial Differential Equations
Non-Classical Symmetries of Partial Differential Equations
Potential Symmetries of Partial Differential Equations
Approximate Symmetries of Partial Differential Equations
Generalized Symmetries
Solution of Coupled Linear Partial Differential Equations
Appendix