* Mathematics for Engineers and Scientists * comprehensively covers the material one would expect for a first-year undergraduate course, as well as more advanced mathematics, including multivariable calculus and Fourier series.

The first edition appeared in 1969, and the book is certainly showing signs of age. It starts in a rather formal manner that could arguably prove off-putting. By page five, we have seen that the set of rational numbers is countable, and in the first example we see a proof that the ratio of the means of two sets of positive data is bounded by the minimum and maximum of the ratios of individual elements from each set.

Contrast this with another textbook on my shelf, aimed at the same students, where the first example is to add 4 to 9.

While this second example arguably goes too far, it is important for authors to take account of the trepidation with which many students approach mathematics, especially those for whom it is not the main subject.

While I applaud Alan Jeffrey for his conviction that the proof of a result can be as important as its application, I fear he is fighting a losing battle.

The book does become more accessible later on, and its target audience will appreciate the thought that has gone into providing physical examples, but there are a number of instances in which, even though the book has reached its sixth edition, the content needs to be overhauled. For example, the chapter on matrices and linear transformations has changed little in 35 years: Cramer's rule is now a historical curiosity, yet it appears as the primary technique for solving linear equations. And in the chapter on numerical analysis, Jeffrey makes the common mistake of associating ill-conditioning of matrices with a small determinant.

The new edition finishes with a cursory chapter on the software packages Maple and Matlab. It should offer, at the very least, a list of useful commands along with the examples provided. And, even though the chapter is new, the versions of the software considered (Maple 8 and Matlab 5) are long out of date.

* Essentials of Engineering Mathematics * offers an alternative perspective on the same material. The book is divided into 86 short sections and one much longer one. Each of the short sections covers the amount of material one would hope to get through in a lecture or two, typically giving a short introduction to the relevant theory and several worked examples. As is appropriate, the examples concentrate on showing how the theoretical techniques can be applied in a mathematical context, conveying the need for students to adopt a flexible approach when problem solving.

Jeffrey's book could be easily adopted as a course text, and the sections can be divided naturally into groups for shorter modules. The final longer section is a word-for-word reproduction of the final chapter of * Mathematics for Engineers and Scientists * , and is equally ineffective here.

Philip Knight is lecturer in mathematics, Strathclyde University.

## Mathematics for Engineers and Scientists. Sixth edition

Author - Alan Jeffrey

Publisher - Routledge

Pages - 994

Price - £29.99

ISBN - 1 58488 488 6

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