Synopses & Reviews
This is the first book which explicitly uses Mathematica (computer algebra system) to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Heretofore time-consuming and cumbersome calculations if done by hand, are much more easily and quickly performed via the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, should be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. This book contains a large number of working examples relating to these applications of Lie's theory. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which provide users with the capability of directly interacting with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool to perform algebraic computations.
Synopsis
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.
Synopsis
This is the first book that uses Mathematica to compute and solve differential equations using Lie's theory. Each section begins with a theoretical discussion of the material; the applications are then presented along with the corresponding Mathematica solutions.
Description
System requirements for accompanying computer disc: Windows 95; Mac; UNIX. Includes bibliographical references (p. [493]-502) and indexes.
Table of Contents
Introduction -Elements of Symmetry Analysis -Derivatives -Symmetries of Ordinary Differential Equations -Point Symmetries of Partial Differential Equations -Non-Classical Symmetries of Partial differEquations -Potential Symmetries of Partial Differential Equations -Approximate Symmetries of Partial Differential Equations -Generalized Symmetries of Partial Differential Equations -Solution of Coupled Linear Partial Differential Equations -Appendix - Index