Just the job if you want to do a little t-shifting

Although society as a whole increasingly shuns it, scientists and engineers need to be fluent in mathematics: it is the language of their trade, and they need more than a phrase book to succeed.

Some books use programmed learning and lots of worked examples to introduce their readers to the world of advanced mathematics. The two books under review do not fall into that category. Both texts are aimed uncompromisingly at students who already have a grasp of mathematics up to and beyond that covered in the first year of a bachelor degree course in science or engineering.

These two books have a lot in common: both are enlarged recent new editions of established textbooks, both are American, both are weighty tomes and both assume considerable mathematical knowledge and skill on the part of the reader. Mary Boas's volume is slightly more user-friendly and chatty in its approach, whereas Erwin Kreyszig's book would work well as an accompaniment to a taught mathematics or engineering course. Kreyszig's is well signposted, with clear indications as to the prerequisites for each chapter and answers to tutorial questions, and chapter-end summaries.

As already suggested, students who struggle with mathematics and need to be spoon-fed will find both these books intimidating, but the mathematically able will find them handy works of reference.

Neither of these books is intended as a pure mathematics textbook. They are aimed, respectively, at physicists and engineers. These professional groups are not interested in mathematics for its own sake; rather, they are interested in maths as a tool for solving problems in their own subject area. But there is very little in either book on the scientific or engineering applications of the mathematical material presented. Both books boast numerous worked examples and tutorial exercises, some with answers, but they do not address specific problems in the fields of engineering or physics. Engineering is a broad church and not all examples would be relevant to all readers, but it would be appropriate to have at least some examples that are relevant to some readers.

Both textbooks are comprehensive in their coverage. Mathematically speaking, if it is not covered here, an engineer or scientist is probably unlikely ever to need to know it.

If you find that you need eigenvectors, d'Alembert's solution, t-shifting and Laguerre polynomials in your life, then either of these books is for you.

Philip Garrison is senior lecturer in structural engineering, Leeds Metropolitan University.