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The student’s introduction to Mathematica
Torrence B., Torrence E., Cambridge University Press, New York, NY, 1999. Type: Book (9780521594615)
Date Reviewed: Oct 1 1999

This text is designed as a companion to conventional textbooks in calculus and linear algebra. It is not intended for standalone use, as it illustrates rather than teaches the mathematics. It consists of two parts: the first two chapters give a general introduction to using Mathematica, and the remaining five chapters illustrate the mathematics. Chapters 3 and 4 discuss functions, graphs, and a variety of algebraic topics, basically the material of precalculus. Chapters 5 and 6 cover the material of univariate and multivariate calculus, respectively, with an emphasis on manipulation in the former and on graphing in the latter. Finally, chapter 7 treats linear algebra as far as vector spaces, eigenvalues and vectors, and linear transformations. We meet just about all the topics in a first course in each of the areas covered, and considerably more than in some first courses.

Generally, the text is friendly and easy to follow. There are no exercises, but there are many examples given in Mathematica code fragments, which are easy to modify so as to incorporate different cases. The examples lean heavily on the trigonometric functions and make relatively little use of the exponential function (and none at all in the precalculus chapters). Thus, the text is clearly intended for science and engineering students rather than for business students. The book includes a fairly complete index of mathematical terms and Mathematica keywords and symbols. Especially in the later chapters, where the mathematics and the Mathematica are more complex, the explanation of the options in the Mathematica commands is by example rather than by description, so the reader would need to refer elsewhere for cases not covered in the text; in some cases the text gives information about using the Mathematica help screens to generate such descriptions. Overall, this is an approachable and helpful text that looks like it has been tested in the classroom.

Reviewer:  Ian Gladwell Review #: CR122473 (9910-0745)
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