In the preface, the authors state:

Maple V By Example bridges the gap which exists between the very elementary handbooks available on Maple V and those reference books written for more advanced Maple users. The reader will find that calculations and sequences most frequently used by beginning users are discussed in detail along with many typical examples. …In addition to serving as a reference, Maple V By Example can also be used as a supplement in courses which take advantage of Maple’s capabilities like calculus, differential equations, linear algebra, and applied mathematics or courses which require these topics as prerequisites.

It is one in a growing collection of texts and manuals designed to help users of the Maple V computer algebra system.

The book consists of eight chapters:

• Getting Started

• Numerical Operations on Numbers, Expressions, and Functions

• Calculus

• Introduction to Sets, Lists, and Tables

• Nested Lists: Matrices and Vectors

• Related Topics from Linear Algebra

• Applications Related to Ordinary and Partial Differential Equations

• Selected Graphics Topics

The text achieves the purposes the authors establish in the preface. It is clearly written and less terse than a manual covering the same topics. A large selection of applications are interwoven to illustrate the use of Maple commands and facilities. The text covers a broad range of topics and, of necessity, does not always treat them in great depth. One exception is the chapter on differential equations, which is 139 pages in length.

I noted at least a dozen minor errors: on page 20, the authors use “e” to denote the base of natural logarithms, when the Maple convention is to use “E”; the variable argument is absent in an example on page 72; in an example on calculating limits on page 83, the independent value is said to be “close to 0,” when it is actually approaching 1; and on page 254, “Stoke’s Theorem” should be “Stokes’s Theorem.”

The ten-page section on linear programming is not well done. The authors introduce “standard forms” for minimization and maximization problems in which the inequality constraints in both cases are in the same direction (“greater than or equal”), which is certainly not standard. The question of whether feasible solutions and optimal solutions to linear programs (and dual linear programs) exist is never covered. In a discussion of writing linear programs using matrix and vector notation on pages 240 and 241, a problem is first called a “minimization problem” and then a “maximization problem.” In an example on page 241, after stating the problem, the authors add a greater-than-or-equal inequality in which all coefficients are 0 and the right-hand side is 0. They never explain what they hope to accomplish by doing this. Maple output on page 242, which should be a vector, has no commas separating components.

The world of mathematics and the world of Maple that the authors discuss are ones where little goes wrong. Inverses of matrices are introduced, but the question of their existence is not covered. Only systems of linear equations that have unique solutions are given as examples, and the reader is never told that systems exist that are, for example, inconsistent. For the most part, only examples that show Maple commands yielding mathematical results, albeit after possibly lengthy computations, are presented. The reader is also given no hint that he or she may run into difficulties using Maple, other than a warning about Maple’s being demanding in the area of syntax. This approach is in distinct contrast to other introductory books on Maple, such as Char et al. [1] and Heck [2], which discuss potential computer algebra pitfalls, such as intermediate expression swell, and give examples of error messages that can arise when using Maple.