Symmetry Analysis of Differential Equations with Mathematica®
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Beschreibung
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.
The author shows how to use Mathematica to quickly perform computations that would be both time consuming and cumbersome if done by hand
Includes a CD-ROM containing Mathematica 3.0 notebooks for interacting directly with the code provided in the book
Also includes the authors proprietary "MathLie" software, which aids in performing algebraic computations
Each section of the book describes the theoretical foundations of the material, then shows the application in connection with Mathematica
The book contains many working examples relating to the applications of Lie's theory
The first publication to offer speedy, computer-algebra based calulations and solutions using Lie's methods and techniques. An invaluable tool for scientists, mathematicians and engeineers, dealing with symmetry analysis of differential equations.
Autor*in
Gerd Baumann
Themen in »Symmetry Analysis of Differential Equations with Mathematica®«
Mathematica Potential algebra calculus computer algebra ordinary differential equation partial differential equation