Many good partial differential equations textbooks are available for applied science and engineering students. What sets this book apart from the others is an attempt to incorporate the use of Mathematica into the presentation and learning of the subject. Potential users of this textbook might first judge it in terms of whether it treats the standard partial differential equations topics, however. It generally does this, and I found the presentation to be clear and accurate. One nonstandard feature of the book is a lengthy two-chapter sequence on the series solution of ordinary differential equations, special functions, and orthogonal polynomials. It would usually be assumed that a student of partial differential equations already had this background from previous study of ordinary differential equations. A second nonstandard feature of the book is a final chapter on inverse scattering, which would not be found in most beginning partial differential equations textbooks.

The big question remaining about the book is whether the use of Mathematica significantly contributes to the presentation and ease of learning of the subject material. The book does not provide a guide to Mathematica, so someone using this book who also wants to use Mathematica needs either to have some previous Mathematica experience or to be prepared to spend some time learning the basic elements of Mathematica from some other source of information. The main uses of Mathematica in the book are for graphics and for aiding in the manipulation of mathematical expressions. Within the informative material, the author provides detailed descriptions of how Mathematica can be used to derive mathematical results and to produce graphs and illustrations. The author also provides many exercises that either require the direct use of Mathematica or have suggestions about how Mathematica could be used to help produce solutions. The main benefits from using Mathematica with a text like this are to eliminate some of the tedious algebra that most students of partial differential equations must deal with and to help with the visualization of solutions to the equations. This book is a guide to obtaining these benefits, and I would recommend that anyone who teaches partial differential equations and whose students have access to Mathematica consider using it. This book might also be of use to people who use partial differential equations in their work and want to learn how to use Mathematica as a tool to work with these equations.