Chemical Education Today
Book & Media Reviews
edited by
Jeffrey Kovac University of Tennessee Knoxville, TN 37996-1600
Mathematics for Chemistry and Physics by George Turrell Academic Press: San Diego, 2002. 408 pp. ISBN 0127050515. $49.95 reviewed by Andrew J. Pounds
When I first looked at Mathematics for Chemistry and Physics my inclination was that the text contained far too much material for the average student to absorb. A certain amount of mathematical sophistication is assumed and the topics seem to span the entire spectrum of mathematical physics. The preface of the book states, “the first three chapters are essentially a review of elementary calculus. After that there are three chapters devoted to differential equations and vector analysis. The remainder of the book is at a somewhat higher level”. This is not a fundamental mathematics book, nor is it intended to serve as a textbook for a specific course, but rather as a reference for students in chemistry and physics at all university levels.” This is a fair assessment of the text. The elementary sections include material on both single and multivariable calculus, and the sections on differential equations include both ordinary and partial differential equations. It is, however, the latter chapters that give this book its particular character. The more advanced chapters start with a treatment of operators and matrices. This is followed by a chapter on group theory and molecular symmetry. Chapter nine is devoted to molecular mechanics and includes such topics as the classification of rotators, internal coordinates, and the G matrix. Chapter ten covers selected topics from probability and statistics, such as Stirling’s approximation and Lagrange multipliers. This is all done within the general framework of statistical mechanics and partition functions. A chapter is then spent discussing Fourier and Laplace transforms, including Green’s functions. The last two chapters in the text are devoted to approximation methods in quantum mechanics and
numerical analysis. Included in the quantum mechanics chapter are sections on perturbation theory and the variational method. The numerical analysis chapter covers such topics as least-squares approximation, numerical integration, and the fast Fourier transform, but is devoid of any algorithms or code for symbolic algebra programs. While there are numerous texts on the market with the general theme of gathering together the most-used mathematical techniques in chemistry and physics, each has a slightly different scope and emphasis. For example, texts specifically targeting undergraduate physical chemistry students will often spend a significant amount of time developing concepts in multivariable calculus, ordinary differential equations, linear algebra, and series. Texts targeting physics undergraduates will typically spend more time developing special functions, operators, and vector calculus. Modern texts targeting both fields generally include sections on numerical analysis. Turrell’s book contains all of these topics, plus introductory matter, partial differential equations, group theory, and 10 appendices, all packed into 408 pages. The treatment is therefore not exhaustive, but the essential concepts are covered. Unlike similar texts, there are few examples of specific problems an undergraduate would see in physical chemistry. Endof-chapter problems are heavy on derivations and proofs. Solutions are provided for most end-of-chapter problems that have a numerical result. Although the author claims that the book is intended as a reference, it is my opinion that, with guidance and direction through a selection of the topics, it could be used as a text either for a one-semester survey course or a rigorous yearlong course in mathematical physics. Turrell’s clear writing style is accessible to undergraduates, and he has labeled the equations for easy reference. Students taking advanced classes in spectroscopy, quantum mechanics, statistical mechanics, or computational chemistry might find this book helpful. Andrew J. Pounds is in the Department of Chemistry and Computer Science, Mercer University, Macon, GA 31207;
[email protected].
JChemEd.chem.wisc.edu • Vol. 80 No. 11 November 2003 • Journal of Chemical Education
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