**MATHEMATICAL METHODS FOR SCIENTISTS AND ENGINEERS,**** by Donald A. McQuarrie, University Science Books, 2003, 1,161 pages, $90 (ISBN 1-891389-24-6)**

RICHARD N. ZARE, STANFORD UNIVERSITY

My enthusiasm for Donald McQuarrie's mathematical treatise is exceeded only by the brevity of this review. After all, how much can you say about an 1,100-plus-page collection of mathematical formulae and associated information in which about 10 equations grace each page? I can say this: McQuarrie has produced a masterpiece that anyone would want to have handy when confronted with the need to perform serious mathematical analyses. It's destined to become a classic reference text.

McQuarrie, an emeritus chemistry professor at the University of California, Davis, is the same author who has given us other classics: "Physical Chemistry: A Molecular Approach," "Statistical Mechanics," and "Quantum Chemistry." His latest work is beautifully illustrated with two-color graphical side bars that emphasize the principles presented in the text. It includes vignettes of the lives of various mathematicians that almost make them seem human. Taken together, these attributes make the book as appealing as any reference work you might imagine on this topic.

Mathematicians have a disgusting habit of hiding the identity of those who perpetrated various mathematical evils that some of us must master to solve important physical problems. This book lifts that veil. Moreover, it invites the beginner to sharpen skills as needed.

The text is authoritative and comprehensive. Beginning with a review of elementary functions of a single variable, the book covers infinite series, integrals, complex numbers and functions, vectors, multivariable functions, vector calculus, curvilinear coordinates, linear algebra, matrices and eigenvalue problems, ordinary and nonlinear differential equations, orthogonal polynomials, Fourier series, partial differential equations, integral transforms, complex analysis, calculus of variations, probability theory, and mathematical statistics. This list will be recognized as what every undergraduate student should master to become mathematically adept. Furthermore, McQuarrie's treatise introduces the reader to various mathematicalsoftware programs that facilitate solving onerous and tedious problems.

If I have any quibbles, one would be that I wish more space were devoted to aspects of statistical analysis commonly encountered in science and engineering. But quibbles aside, I am grateful that this book has arrived to join the pantheon of needed and treasured reference texts.