Applied Mathematics for Physical Chemistry is the second edition of this text. The first appeared in 1974. The goal of this edition is to bridge the gap between mathematical theory and its application for students being introduced to physical chemistry at the undergraduate level. An almost universal problem faced by undergraduate p-chem teachers is that many students either have a weak background in the mathematical concepts and techniques required for physical chemistry, or they find it difficult to see how their previous mathematical training applies to p-chem. This text is compact enough to function as a supplementary resource that provides a review of or introduction to the mathematics students need to get past this hurdle and concentrate on the essential scientific theory being presented.

The first five chapters review basic mathematics: coordinate systems, functions and graphs, logarithmic and exponential functions, and differential and integral calculus. The next four chapters introduce the most important mathematical concepts that form the foundation for current undergraduate physical chemistry courses: differential equations, infinite series, vector and matrix algebra, and operators. The last two chapters are entitled "Numerical Methods and the Use of the Computer" and "Mathematical Methods in the Laboratory". There are four appendices: a Table of Physical Constants, Integral Tables, more detailed discussions of the transformation of the Laplacian operator to spherical polar coordinates, and Stirling's approximation.

I think the text succeeds quite well in its intended purpose. In each chapter, the theoretical definitions and concepts are nicely integrated with an example or two drawn from a relevant topic in chemistry. Thus the "languages" of mathematics and chemistry are brought together so that a student will see how one is derived from the other. At the same time, the length of each chapter is kept to a minimum. I think this is also important in that it allows a student to quickly consult a chapter for help with a concept without being intimidated by too much information. Students are already confronted by p-chem texts that run between 800 and 1000 pages. A supplementary text that provides too much background or theory will make most students feel as though they do not have the time to sift through the text to find where their own question is addressed. This text should avoid this scenario.

Overall I would recommend that teachers of physical chemistry consider Barrante's text for their classes. It should be noted, though, that this is a text written for the undergraduate student at an undergraduate level. The material in the first five chapters is all review of material they should have been exposed to in prerequisite math courses or other chemistry classes. In a few places I think Barrante goes back a bit too far in his review of the basics (graphing functions, deriving the quadratic equation), but this does not happen too often and is not a serious complaint. I liked the discussion of error propagation in Chapter 12, which, by the way it was presented, should be helpful to students in many of their laboratory courses. I am not sure how useful the section introducing computer programing concepts in Chapter 11 will be, since there are so many commercial spreadsheet-type programs now available which can accomplish the same function without having students "write code".

The 2nd edition of Barrante's text may be compared with one other text, R. G. Mortimer's Mathematics for Physical Chemistry (Macmillan, 1981), when a decision about a supplementary mathematics resource is made. Mortimer's text is somewhat longer but is also a good alternative. Some recent physical chemistry texts now provide very brief "math chapters", which also attempt to address this issue (McQuarrie and Simon, Physical Chemistry [University Science Books, 1997]).