Choice Review

This book was written by a large group of authors under the umbrella of the Harvard Calculus Consortium. The authors are best known for their commercially successful but controversial introductory calculus textbook, Deborah Hughes-Hallett, Andrew M. Gleason, et al. Calculus (1994). The book under review is intended for use in a multivariable calculus course at the sophomore level. Like its predecessor, this book was developed as a "reformed" text with support from the National Science Foundation. The traditional topics are covered, including partial derivatives, optimization problems, parametric curves and surfaces, and the theorems of Green, Gauss, and Stokes. The presentation could hardly be less traditional. As in their previous book, the authors present each topic geometrically, numerically, and algebraically. Examples generally precede definitions and statements of theorems. Proofs are presented in an informal fashion. A more traditional book, like Jerrold E. Marsden and Anthony J. Tromba's, Vector Calculus (4th ed. 1996) covers most of the same topics, but the presentation of theorems, proofs, and definitions is much more formal. Lower-division undergraduates. B. Borchers; New Mexico Institute of Mining and Technology