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e-Book Symmetry Analysis of Differential Equations with Mathematica download

e-Book Symmetry Analysis of Differential Equations with Mathematica download

by Gerd Baumann

ISBN: 0387985522
ISBN13: 978-0387985527
Language: English
Publisher: Springer; 2000 edition (April 20, 2000)
Pages: 521
Category: Mathematics
Subategory: Math Science

ePub size: 1917 kb
Fb2 size: 1562 kb
DJVU size: 1847 kb
Rating: 4.5
Votes: 642
Other Formats: doc lrf mobi mbr

The study of symmetries of differential equations is an old subject. 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 study of symmetries of differential equations is an old subject. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. 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 . note books.

A comprehensive introduction to the applications of symmetry analysis to differential equations. These applications, emerged from discoveries by Sophus Lie, can be used to find exact solutions and to verify and develop numerical schemes. The book includes both theoretical considerations and practical applications of use to physicists, chemists, mathematicians and engineers. There is a CD-ROM included with examples.

Symmetries of Ordinary Differential Equations. Bibliographic Information. Symmetry Analysis of Differential Equations with Mathematica®. The electronic supplement by Eric Bynum and Gerd Baumann contains revised instructions that include more specific instructions for each of the major platforms and clear up some confusing sections of the original documentation.

Instead of this book I recommend "Introduction to Symmetry Analysis" by B. Cantwell, which is much more readable and provides a Mathematica . If you know Mathematica 3 or later, a little of differential geometry, is a good way to do symmetries in differential equations. Cantwell, which is much more readable and provides a Mathematica package. 20 people found this helpful. 3 people found this helpful. 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

Автор: Gerd Baumann Название: Symmetry Analysis of Differential Equations with Mathematica® .

oceedings{O, title {Symmetry Analysis of Differential Equations with Mathematica}, author {Gerd Baumann}, year . The symmetry methods discussed are realized in a Mathematica packag. ONTINUE READING.

oceedings{O, title {Symmetry Analysis of Differential Equations with Mathematica}, author {Gerd Baumann}, year {2000} }. Gerd Baumann. We will discuss three different methods for finding symmetry solutions based on the Frechet derivative common to each procedure. The methods discussed are Lie's standard procedure of symmetry analysis, the nonclassical method, and the derivation of potential symmetries.

Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations.

The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will 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. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact 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 in regard to performing algebraic computations.
Comments:
Steep
I bought the book, but the CD- ROM did not come together. I need it for my work.

net rider
Before giving my opinion I would like to point out that there is a very negative review of this book by Dr. P.A. Clarkson. It appered in SIAM Review, Vol. 43, No. 3, pp. 549-581.

Now for my opinion.

I am doing research in nonlinear PDEs. What I need is a good Mathematica package to take me through the tedious calculations. Unfortunately, MathLie package included with the book does not meet my needs. I have often encounterd very cryptic error messages produced by the package internal functions. I could not find the root causes of those errors, because these functions are not accessible. This makes the results of the calculations suspect. In some cases they do not agree with published results. Dr. Clarkson in his above-mentioned review reports similar experience.

Most importantly, the book really does not help to interpret the output produced by the package. The online help is very inadequate.

I cannot recommend this book as either a textbook (too cryptic) or a research reference/tool (results are suspect).

In summary, I agree with Dr. Clarkson that "this book should have never been published". I only wish I saw his review before making a mistake of purchasing it.

Instead of this book I recommend "Introduction to Symmetry Analysis" by B. Cantwell, which is much more readable and provides a Mathematica package.

Prorahun
I regret the time and money expended in acquiring the following information. In no way can I recommend this book to any reader.
This work is incoherent and reflects the incoherence of the design of the MathLie Mathematica Package. The text is neither an adequate introduction to the package nor a suitable reference. Descriptions of functions are locally incomplete and globally scattered throughout the book. Only after considerable searching does one find that, in fact, there is little functionality for the solution of any but the most trivial systems.
As a tool to learn applications of Lie Groups to Differential Equations, this text is useful only insofar as it represents the thinnest introduction to the material, suitable neither for the expert nor the novice.
As a tool to expand the capabilities of Mathematica, it is a pointless exercise in using essentially undocumented encrypted code with no evident organizational principle. One may well do better to seek help from a divining rod.

Crazy
A good book. If you know Mathematica 3 or later, a little of differential geometry, is a good way to do symmetries in differential equations.

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