Chemical Education Today edited by
Book & Media Reviews
Jeffrey Kovac University of Tennessee Knoxville, TN 37996-1600
Mathematical Methods for Scientists and Engineers by Donald A. McQuarrie University Science Books: Sausalito, CA, 2003. 1184 pp. ISBN 1891389246. $90 reviewed by Jeffrey Kovac
There are many “mathematics for scientists” books available. Leaving aside those written for the general chemistry market, they range from those designed as a supplement for an undergraduate physical chemistry course, such as Mortimer’s excellent Mathematics for Physical Chemistry (1); to texts for the standard year-long graduate course taught in most physics departments, such as the venerable book by Margenau and Murphy (now out of print) (2); and the widely-used volume by Arfken, Weber, and Weber (3). McQuarrie’s new book fits into the latter category, although selected chapters are appropriate for students taking a junior- or senior-level physical chemistry course. McQuarrie is both an experienced textbook author and a distinguished theoretical chemist, and he has used his twin talents to produce an outstanding book. Although this is primarily a book for people who use mathematics, it introduces the necessary theorems to justify the methods and to show their limits. For example, it is important to know when the order of integration can safely be interchanged, and McQuarrie provides the relevant theorems in Section 1.9. Overall, the book does an excellent job of negotiating the difficult territory between pure mathematics and applied mathematical techniques. In Chapter 1, a review of basic calculus, and Chapter 2, on infinite series, I recognized a number of theorems that were proved in my own freshman calculus course, such as the mean value theorem, and the various tests for convergence of series. A number of proofs are outlined using ␦,ε and ε,N methods, but most of the book is a clear and detailed exposition of applied mathematics. This is a comprehensive text. In 22 chapters and more than a thousand pages McQuarrie covers almost all the important mathematical methods used by physical scientists and engineers: calculus, infinite series, vector calculus, linear algebra and matrices, special functions, complex variables, or-
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dinary and partial differential equations, Fourier series, and integral transforms. I was delighted to see chapters on stochastic processes and mathematical statistics, topics often omitted from comparable texts. Unfortunately, there is no discussion of the mathematics of group theory, even the simple symmetry point groups that are so important in chemistry, nor of graph theory or any other topic in discrete mathematics. Since good expositions of these topics can be found elsewhere, this is a minor quibble. Every author has to be selective, and this is already a very long book. McQuarrie believes, quite correctly, that the only way to really learn mathematics is by solving problems, so this book is loaded with problems. Every section is followed by at least ten problems. Most are traditional “pencil and paper” problems, but others require the use of a computer algebra system, such as Mathematica, Maple, or MathCad. Answers to selected problems are given at the end of the book, and a solutions manual is available. The book is nicely designed with attractive two-color graphs and figures to illustrate and amplify the equations. It is written in the clean, straightforward prose that characterizes McQuarrie’s other books. There is more than enough material for a rigorous two-semester course, but it could be selectively covered in a single semester. In either case the students will acquire an excellent reference book. I certainly will recommend it to students and colleagues who want to learn, or relearn, one of the topics in the book. I will put it in a place on my bookshelf where I can easily reach it. I am sure I will refer to it often. Literature Cited 1. Mortimer, Robert G. Mathematics for Physical Chemistry, 2nd ed.; Academic Press: San Diego, 1999. 2. Margenau, Henry; Murphy, George M. The Mathematics of Physics and Chemistry, 2nd ed.; Krieger Publishing: Huntington, NY, 1976. 3. Arfken, George B.; Weber, Hans; Weber, Hans-Jurgen. Mathematical Methods for Physicists, 5th ed.; Academic Press: San Diego, 2000.
Jeffrey Kovac is in the Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600;
[email protected] Vol. 81 No. 10 October 2004
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Journal of Chemical Education
1425
