This book by Robert de Levie is a thorough and comprehensive how-to guide to the use of the Excel program on common numerical tasks in physical science. It starts with a chapter that surveys the capabilities of the Excel program itself. It then continues with three chapters of progressively increasing sophistication on the method of least squares, followed by single chapters on Fourier transformation, convolution and deconvolution, and numerical solution of differential equations. The final four chapters are given over to the writing of macros and the author's presentation of the many macros he has developed in the course of solving the problems illustrated in the book. Readers should be aware that all of these macros, as well as the numerical data used in many of the examples, are also available in computer-readable form from the publisher's web site and, in fact, are available to purchasers and nonpurchasers alike.
I should acknowledge at the outset that I am very much NOT a fan of Excel. However, the program is by now so firmly established that there is little doubt of the value of the contents of this book to many in the intended audience of scientists and engineers. Moreover, there is also plenty of value for those of us who prefer to use computational tools other than Excel. Since my own primary interests relative to this book fall within the chapters on least-squares methods, that is where I will direct my specific comments.
As already noted, the book is about computations, not about theory, so although key working equations are often presented, they are seldom derived. Thus a beginner wanting to understand the method of least squares might want to consult another source to complement the "nuts and bolts" provided by the examples illustrated here.
Chapter 2 is devoted to the simplest of least-squares (LS) problems, unweighted fitting to a straight line (including one forced to go through the origin). This chapter also introduces the important topic of propagation of error (called propagation of imprecision by the author in an attempt to improve the terminology). A number of common applications are considered, the most important of which is probably the role of linear LS in calibration in analytical chemistry. This is, incidentally, an application where the common textbook expressions for error propagation lead to incorrect estimates of the imprecision; but de Levie "does it right."
Chapter 3 continues with linear LS, but now involving fitting to functions more complex than a straight line and often involving three or more adjustable parameters. (Note that the "linear" in linear LS refers to the manner in which the adjustable parameters occur in the fit function, not to the shape of the function itself; some authors refer to this as "multilinear.") The coverage begins with fitting to polynomials and is later extended to orthogonal polynomials. Toward the end of the chapter, weighted LS is introduced; this is needed to deal with the problem of transforming nonlinear fit relationships into linear ones, like exponentials (log transformation) and hyperbolic relationships (reciprocal transformation). Most of the examples in this chapter are from analytical and physical chemistry and are often encountered in the chemical teaching literature. These include the analysis of diatomic spectroscopic data (I2 and HCl), the analytical problem of estimating species abundances from UV-visible spectra of mixtures, and the treatment of enzyme kinetics data.
Chapter 4 turns to nonlinear LS, in which iterative methods are needed to obtain the solutions to the minimization problem at the heart of LS. The tool for accomplishing this task in Excel is the Solver routine. Solver has one glaring limitation, namely the failure to provide the statistical errors in the adjustable parameters. De Levie has solved that problem with his own macro, SolverAid. The capabilities of these routines are illustrated on a number of examples, again mostly from the realm of analytical chemistry and spectroscopy. Among the more unusual examples are fits of titration data, of discontinuous functions, and of continuous functions taken piecewise. Toward the end are included some illustrations of the performance of Solver on some benchmark nonlinear fitting problems provided by NIST (National Institute for Science and Technology).
I have personally checked many of the examples illustrated in these three chapters using other methods, and I can vouch for their general validity. In a few cases there are errors, but many of these have been corrected by the author since the first printing of the book. Users should consult the publisher's web site for a listing of these.
In summary, this work will prove a valuable addition to the bookshelves of Excel-oriented "number-crunchers." For those who prefer programs other than Excel, the examples can still provide useful instruction. For this group, the Excel material is of no use but also no real impediment. For those who hope to learn both data analysis and Excel at the same time, from "scratch," I doubt that this book will fill the bill: You'll probably need to start with more elementary treatises in both areas. I must admit that my aversion to the Excel program itself and its heavy focus in this book is what prevents me from giving the book the maximum rating.