Customer Reviews

Symmetry Analysis of Differential Equations with Mathematica

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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.

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.

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.