# Symmetry Analysis of Differential Equations with Mathematica®

• Gerd Baumann
Book

1. Front Matter
Pages i-xii
2. Gerd Baumann
Pages 1-5
3. Gerd Baumann
Pages 6-36
4. Gerd Baumann
Pages 37-95
5. Gerd Baumann
Pages 96-215
6. Gerd Baumann
Pages 216-364
7. Gerd Baumann
Pages 365-391
8. Gerd Baumann
Pages 392-403
9. Gerd Baumann
Pages 404-423
10. Gerd Baumann
Pages 424-456
11. Gerd Baumann
Pages 457-482
12. Gerd Baumann
Pages 483-492
13. Back Matter
Pages 493-521

### Introduction

The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica 3.0 note­ books. The entire printed version of this book is available on the accompanying CD. The text is presented in such a way that the reader can interact with the calculations and experiment with the models and methods. Also contained on the CD is a package called MathLie-in honor of Sophus Lie---carrying out the calculations automatically. The application of symmetry analysis to problems from physics, mathematics, and en­ gineering is demonstrated by many examples. 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 improve­ ments 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.

### Keywords

Mathematica Potential algebra calculus computer algebra ordinary differential equation partial differential equation

#### Authors and affiliations

• Gerd Baumann
• 1
1. 1.Department of Mathematical PhysicsUniversity of UlmUlmGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-2110-4
• Copyright Information Springer-Verlag New York 2000
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-7418-6
• Online ISBN 978-1-4612-2110-4
• Buy this book on publisher's site