Symmetry Analysis of Differential Equations with Mathematica®

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...

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Main Author: Baumann, Gerd
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2000, 2000
Edition:1st ed. 2000
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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100 1 |a Baumann, Gerd 
245 0 0 |a Symmetry Analysis of Differential Equations with Mathematica®  |h Elektronische Ressource  |c by Gerd Baumann 
250 |a 1st ed. 2000 
260 |a New York, NY  |b Springer New York  |c 2000, 2000 
300 |a XII, 521 p. 56 illus  |b online resource 
505 0 |a 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 of Partial Differential Equations -- Solution of Coupled Linear Partial Differential Equations -- Appendix -- Index 
653 |a Applied mathematics 
653 |a Mathematical and Computational Engineering 
653 |a Chemometrics 
653 |a Engineering mathematics 
653 |a Algebra 
653 |a Numerical and Computational Physics, Simulation 
653 |a Algebra 
653 |a Numerical analysis 
653 |a Physics 
653 |a Mathematical Methods in Physics 
653 |a Numerical Analysis 
653 |a Math. Applications in Chemistry 
710 2 |a SpringerLink (Online service) 
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989 |b SBA  |a Springer Book Archives -2004 
856 |u https://doi.org/10.1007/978-1-4612-2110-4?nosfx=y  |x Verlag  |3 Volltext 
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520 |a 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