Book Review  

Applied Mathematics for Physical Chemistry

 Reviewed by
Hugh Cartwright
Chemistry Department Oxford University, South Parks Road, Oxford England OX13QZ
hugh.cartwright@chem.ox.ac.uk

Applied Mathematics for Physical Chemistry (2nd ed.) by James R. Barrante. Prentice Hall: Englewood Cliffs, New Jersey (1998), 227 pages. ISBN 0-13-741737-3.

When starting a college chemistry course, many students think they know which areas of the subject will cause the greatest difficulty: memorization of the properties of numerous inorganic compounds, perhaps, or understanding the curious world of quantum mechanics.

In reality, the most serious problems are often those presented by something much more prosaic - mathematics. A facility with this subject is vital in many areas of chemistry, none more so than physical and quantum chemistry. Barrante's slim paperback seeks to provide the essentials without which almost any honors-level chemist will struggle.

This is the second edition of a fairly venerable text (the first edition appeared in 1974); it seems that the mathematical needs of chemistry undergraduates change only slowly! Applied Mathematics for Physical Chemistry is very much a mathematics text, rather than a chemistry text. Examples and problems are predominantly abstract and mathematical, but the topics themselves are chosen for their immediate relevance to chemistry, and little is discussed that would not be of value in a typical honors-level science course. Thus, all the topics one would expect to find are present: calculus, operators, matrices, differential equations, errors, and more. Explanations are brief, but this is less a textbook, more a "...how to do it review book" as the author puts it. In consequence, it is not really suitable for students with a very weak background in mathematics, but will without doubt be of value to those whose mathematical knowledge, while once good, has begun to drift away through age or under-use.

The text has been revised for the second edition, but the new chapter on computer programming in BASIC seems to me to be of little value. Many students are familiar with programming by the time they reach a college or university. Once there, many more will be taught to use spreadsheets or packages such as MathCad, which will do most of what the book discusses, in a way that avoids the necessity of learning a formal computer language. There are, in any case, many excellent books available on programming, which cover the subject in a more satisfactory way that Barrante can manage within the length limitations imposed by a single chapter.

The appendices too are something of a disappointment. A useful list of standard integrals is not matched by others of similar value. There is no appendix of differentials for example, or trigonometric relations, or expansions. Much of this material is to be found scattered through the book, but I would have preferred to see the space allocated to programming instead given over to more comprehensive appendices.

However, these are minor reservations. The writing is clear, the diagrams are uncluttered and plentiful, the level of detail is well-judged and the choice of topics appropriate. In contrast to the mid-1970s, when this book first appeared, several texts are now available which deal with the mathematics of relevance to chemists. This remains one of the best, and will be of value to both students and their teachers.