Practical serving of baked beans

The market for introductory texts in mathematics at undergraduate level is so saturated that authors have to work hard to offer their audience something different. These four books have achieved this, as indicated by their widespread adoption on university courses.

The elegantly written Modern Engineering Mathematics distinguishes itself by living up to its title's promise and offering a contemporary view of the subject. Of all these books, it gives the most thorough treatment of numerical methods for solving engineering problems, going as far as to consider the pernicious effects of rounding error in the opening chapter; and it gives short shrift to outdated topics such as Cramer's rule.

The book contains less advanced material than the other volumes, allowing the author room to cover the subject in great detail. The short introductory sections to each chapter are a welcome feature, providing historical background and pointing out significant areas of application. The book is not weighed down by theory, and practical applications - from the supply of baked beans in a roadside cafe to the take-off of an aircraft - are used as illustrative examples wherever possible.

Judged by its title, Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers could not be clearer as to whom it is aimed at. However, the book could be used by any student of engineering. Specialisation is limited to a few topics, such as in the comprehensive treatment of integral transforms.

The book tries its hardest to avoid getting caught up in theory, although this means that some statements can be interpreted ambiguously (for example, the discussion of indices does not deal with negative numbers adequately). In general, the exposition is sound, and practical examples are used throughout, particularly from the areas described in the book's title.

Both the above books are now in their third editions and have changed little in terms of content. The most significant change is in appearance, which is compromised by the use of a thinner and less durable paper.

The authors of Mathematical Techniques deliberately segregate examples involving scientific applications. They argue that the early introduction of such material can add to the confusion of some students. The result is a more conventional mathematics book, but it is still suitable for students in physics or engineering.

Again, this edition has undergone cosmetic change. It, too, has been reset, but in this case the look and feel of the book have improved (at the expense of introducing a few typographical errors). There are also significant changes in content in the opening chapter, where the foundation material has been expanded usefully. The authors do not attempt to dodge theoretical hurdles. They are careful to explain many of the less intuitive properties of functions and to highlight generalisations without becoming overly abstract.

By deciding to keep chapters as short as possible, the authors have produced a rather arbitrary division of material in places. Most chapters jump straight into their subject without any words of introduction, which can be disconcerting and may make the book less useful for independent study.

Finally, Mathematical Methods for Physics and Engineering contains a substantial body of new material. A new preliminary chapter has been added, covering topics such as proof by induction, indicating the more traditional nature of this book in comparison with the others. It demands a high level of mathematical sophistication from its readers, making it less appealing as an accompaniment to a first undergraduate course. However, it covers a broad syllabus, finding room for a chapter on group theory along with more standard topics in advanced applied mathematics. It would be an ideal reference for well-motivated students in physics.

All the books have an appropriately wide selection of exercises for students to attempt, with hints or solutions offered to almost all of them. Additional support is offered by the two Prentice Hall books in the form of a CD-Rom containing 1,000 diagnostic questions.

The CD would have benefited from more thorough testing before being released, as it has a much less polished feel than the books it accompanies. The interface is particularly ugly, requiring the user to pursue pop-up windows around the screen; and the text is blown up to fill the screen, which results in a blurred image and prevents the use of any other application on the computer. However, the feedback for wrong answers works well, with detailed solutions available for each question.

Philip Knight is lecturer in mathematics, University of Strathclyde.