BOOK REVIEWS sity, the ?)wss-centered diffusion flux must be considered, which implies that the appropriate concentration variable is the mass fraction. It is often necessary to use the mass-centered system for another reason also: When chemical reaction occurs, moles are not conserved, whereas mass is; the mass fraction also recommends itself when the molecular weight of the diffusing substance is uncertain, as in the case of a hydrocarbon fuel diffusing toward a flame. The reviewer did not find in the book any statement of the above views (which may be wrong) or of any alternative recommendations for dealing with problems of this kind, which arise in almost every practical application of masstransfer theory. It would, however, be entirely unfitting to close this review on a critical note. The reviewer has therefore saved until the end an expression of his profound admiration for a work which is scholarly, lucid, and elegant. The authors have taken almost unprecedented pains to aid the student's labors; careful definitions, helpful notation, lively examples, ancl handsome printing make this work one of which the authors, and the publishing house, can take a well-justified pride. Students, teachers, and industrial scientists will be grateful to them for a long time to come.

This volume contains 21 chapters on various topics in applied mathematics. The chapters have been written by 20 individuals, each of whom has been involved with the applications of mathematics, mostly in the physical sciences and engineering. The following topics are discussed in one or more chapters: basic analysis, vectors, tensors, complex variables, ordinary differential equations, partial differential equations, special functions, integral equations, transform methods, asymptotic methods, perturbation methods, linear algebra, functional approximation, numerical analysis, optimization techniques, probability, and statistics. Also included are chapters on several particular areas of application, namely, oscillations, wave propagation, and formulation of mathematical models. The volume is not a handbook in the usual sense, that is, it is not a collection of tables and formulas. Instead, each chapter represents the author's summary description of the chapter topic, with emphasis on the ideas and techniques of potential value in problem solving. Motivation is provided from the applied sciences for most of the topics discussed and the presentation is generally descriptive, rather than formal. Based on a close look at several of the chapters in areas most familiar to me, the treatment is quite complete. The chapters have been prepared independently, without cross-referencing, so that some topics are covered more than once, usually from different points of view. The volume does include an extensive index of 32 pages, so that the place in which any particular topic is considered can easily be determined. For example, the Wiener-Hopf method can be found in the chapter on transform methods, variational methods are discussed mainly in the chapters on ordinary differential equations and on optimization, and the finite element method is briefly introduced in the chapter on partial differential equations of second and higher order. The coverage appears to be quite complete within the branch of mathematics commonly termed analysis. The rationale for including two chapters on specific applications, namely, wave propagation and oscillations (nonlinear

A Brownian dynamics model for the backbone chain of a macromolecule is developed as a system of linked rigid bodies so that constraints on valence angles and bond lengths are satisfied exactly. For comparison, a corresponding flexible model is developed in which bond lengths and valence angles are held nearly constant by strong harmonic potentials. Equilibrium properties and barrier crossing rates are examined theoretically and by computer simulation of both models, with differences arising due to the presence of constraints in the rigid case. A compensating potential based on the metric determinant of unconstrained coordinates in the rigid model is found to eliminate the effect of constraints. Barrier crossing rates in the transition state approximation are studied when a force fixed in space is applied to the end atoms of the three-bond chain. An exact transition state rate formula developed for this case predicts curved Arrhenius plots of barrier crossing rates; this result is confirmed by computer simulation.

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