Hold the rigour but make sure those worked examples work

What are you looking for in a student textbook on engineering mathematics? Few nowadays would go for serious mathematical rigour. As an applied mathematician teaching engineering students, I look for the presentation of methods supported by plausible (not necessarily rigorous) derivations of the results, good worked examples and exercises, with applications to real-life engineering problems.

These two books target different parts of the market. John Bird's book is aimed at students progressing through BTec higher nationals (the text is organised in line with units within BTec syllabuses) to the early years of a degree programme. Glynn James's book is intended as a second-level text for undergraduate engineering students. Both books follow on from companion texts, and both cover a broad curriculum of analytical, numerical and statistical methods.

The strength of Bird's book is in its detailed worked examples and extensive exercises posed in a variety of contexts. What is lacking, for my taste, is any attempt to prove or even justify many of the standard methods and formulas. This may give the impression that mathematics for engineers is a series of unconnected results that simply have to be memorised and applied. Given that this is the third edition of the book, it is disappointing to find a relatively large number of typographical errors and surprising to find instances in which the use of notation and explanation of basic concepts is lacking - for example, the introduction to probability in chapter 32 needs some revision. Students will like the worked examples and exercises, but I would want to give careful guidance to ensure that appropriate use is made of this text.

James's book sets out to sell mathematics to the engineering student. Each chapter starts with a motivational introduction and contains one or more sections on engineering applications. Where appropriate, proofs (or at least justifications) of formulas and methods are given.

Overall, however, statements and derivations of results tend to be a bit terse, and often diagrams are too small to allow easy interpretation. In this second edition, an introductory section on vector spaces is added, but, it is not sufficient for a student who is meeting this subject for the first time. On the other hand, the text has plenty of worked examples and exercises that range from the routine to ones that should extend and deepen understanding.

Neither book strikes me as the definitive text for its intended market - but do such texts exist? Both have potential, and careful proof-reading and thoughtful revision of some parts in advance of future editions will further enhance their usefulness.

D. F. McGhee is senior lecturer in mathematics, University of Strathclyde.