John Bird’s Higher Engineering Mathematics is designed primarily for students taking a Higher National Certificate or a Higher National Diploma but covers a sufficiently broad syllabus to be useful for degree students, too. Indeed, many students will appreciate the fact that the book is very light on theoretical discourse, concentrating instead on worked examples that make it particularly useful as a revision tool.
It considers a wide variety of areas in engineering to give the material some context (from the calculation of radii of gyration to the design of switching circuits). Bird has clearly used his imagination in designing examples for statistical testing (although the number that concern component failure and employee absenteeism may be a worrying sign for British industry).
In places, the book has a distinctly retro feel which, while charming when indicator diagrams for steam engines are being discussed, is worrying when some of the methods advocated for numerical solution are long past their sell-by date. The decision to set the text with two columns to a page gives the book a rather cluttered feel and is frequently abandoned to accommodate large diagrams, though it does mean that the book is considerably shorter than the others under review.
There is an accompanying website including remedial material in basic algebra. It is a pity this has not been integrated into the book, as it is an area where students are notoriously weak.
Mathematics for Engineers by Anthony Croft and Robert Davison acknowledges this; the most significant change in the new edition is the expanded treatment of foundation material. The authors claim to adopt an interactive approach to learning. They do this by including many exercises where the reader is expected to fill in only a few intermediate steps.
The reader is expected to cover up the correct answer while working out their own and this (literally) hands-on approach certainly gets you involved. The book contains more theory than Bird’s, but not enough to be intimidating to any but the weakest student. The material covers all you would expect from an introductory university text, although its treatment of numerical techniques is rather curt, and certain topics (such as interval notation and the delta function) are introduced, never to be seen again.
The book also contains a CD-Rom with 1,000 diagnostic questions. Disappointingly, this has not been revised for the new edition of the book and suffers from a poorly designed interface with blurred text and an unnecessarily complicated method of response.
Advanced Modern Engineering Mathematics by Glyn James has in-depth coverage of material that is only touched on in the other two texts, focusing on topics such as integral transforms and the solution of differential equations. It also pulls no punches in its theoretical treatment of the subject.
A sizeable team of authors has been assembled to cover the often highly specialised content, much of which anticipates postgraduate study. Each chapter adopts a common structure, starting with a brief motivation and concluding with an extended discussion of particular engineering applications, which means that despite the number of authors, the book has a single voice.
The book contains only 11 chapters, allowing the authors room to include unusual subjects in an undergraduate text, such as matrix functions and techniques for solving stiff differential equations. There is also a strong emphasis on the use of software packages, going so far as to include Matlab code throughout. This all means that the inclusion of “modern” in the title is warranted, even though the businesses that feature in the chapter on optimisation appear to have been immune to the effects of inflation!
Philip Knight is lecturer in mathematics, Strathclyde University.
Higher Engineering Mathematics. Fourth edition
Author - John Bird
Publisher - Newnes
Pages - 704
Price - £22.95
ISBN - 0 7506 6266 2