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Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, 1st edition

John H. Hubbard and Barbara Burke Hubbard

CHOICE: Current Reviews for Academic Libraries is published by the American Library Association. A reader survey ranked it "the best short critical evaluations of new titles available anywhere".

The following review of the first edition appeared in the June 1999 issue. It is reprinted with permission from CHOICE, copyright by the American Library Association.

"The decade of the '50s saw the emergence of a stunningly lucid series of Princeton University seminar notes, most notably by John Milnor, recording the remarkable advances in differential geometry then being achieved by such as Atiyah, Bott, Chern, Hirzebruch, Thom, and of course Milnor himself.

Not long after there appeared a draft of Advanced Calculus by Nickerson, Spencer, and Steenrod (NSS), though it seems never to have been truly published; this brought down to the sophomore level the understanding of those marvelous Princeton seminar notes.

The appearance of NSS marked the beginning of a small but important countercurrent to the implacable flow of overweight, traditional, rote, mechanical, mainstream multivariable calculus books — one thinks fondly of Michael Spivak's Calculus on Manifolds (1965); Casper Goffman's Calculus of Several Variables (1965); Wendell H. Fleming's Functions of Several Variables (1966); John W. Woll Jr.'s Functions of Several Variables (1966); and Lynn H. Loomis and Shlomo Sternberg's Advanced Calculus (1968).

The book under review is the latest stellar manifestation of this welcome trend. Like its predecessors, it deftly weaves into its exposition of multivariable calculus linear algebra, differential forms, and smooth manifolds. Unlike them, it also exploits today's calculator- and computer-aided symbolic computation and graphical display capabilities. Superb on all counts! Undergraduates through professionals "— F.E.J. Linton, Wesleyan University

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