In the past few years, there has been a proliferation of books that describe how modern mathematical software (Macsyma, Maple, Mathematica, and so on) can be included in the mathematics curriculum. This book, which describes how Maple V can be used to solve problems in elementary differential equations, fits into this category. The organization of the book is similar to that of a textbook for a course in this area. Topics include first-order equations, higher-order linear equations, Laplace transforms, systems of linear equations, eigenvalue problems, elementary partial differential equations, elementary numerical methods, and applications. Each topic is described briefly, and the Maple V commands used to obtain solutions to problems are given. In most instances, the commands described are those that directly obtain graphical or formula solutions, as well as those that perform various steps (such as differentiation, integration, substitution, and simplification) in the solution process.

The book is most useful as either a reference book or a supplementary text. The main advantage of the book is that one can look up nearly any topic and quickly locate the Maple V commands that apply. In many cases, it is not necessary to read earlier sections, since the examples of the use of commands in later sections are sufficiently detailed. The book does assume some experience with Maple V, however. For students without this background, an appendix contains a few suggestions for using the software and a brief introduction to the online tutorial that comes with the system. Even so, these students will need additional instruction to effectively use the software.

While I found the book useful and interesting, it does have some limitations. First, although the book includes mathematical descriptions of the standard topics in differential equations, it is not suitable as a primary textbook, since some descriptions are too brief and there are no exercises. Second, it is strictly a how-to book and little consideration is given to the reliability or limitations of the software. With a little experimentation, one quickly discovers there is more to intelligent use of the software than the authors suggest. Although it is easy to give examples where the software responds with unexpected or inappropriate results, the authors rarely mention why this is so or what to do when it happens. Third, the book is overly repetitive. For example, the index contains over 80 references to the use of the dsolve command, which obtains formula solutions to differential equations. Many of these examples are similar and provide no additional information about the use of command. On the other hand, the authors do not give a comprehensive description of dsolve, with a summary of its options, capabilities, and limitations. Finally, a thorough proofreading would have caught a few instances of Maple’s latex command (which creates code for the \LaTeX document preparation system) that were inadvertently left in the text (pp. 6, 94, and 111). Indeed, the first Maple V example is confusing, since it contains one of these commands.

The authors have written a similar book [1] that illustrates how the Mathematica software is used to solve problems in differential equations.