Starting Points.- Geometry of Linear Maps.- Approximations.- The Derivative.- Inverses.- Implicit Functions.- Critical Points.- Double Integrals.- Evaluating Double Integrals.- Surface Integrals.- Stokes’ Theorem.
James J. Callahan is currently a professor of mathematics at Smith College. His previous Springer book is entitled The Geometry of Spacetime: An Introduction to Special and General Relativity. He was director of the NSF-funded Five College Calculus Project and a coauthor of Calculus in Context.
From the reviews: "Many concepts in calculus and linear algebra have obvious geometric interpretations. ... This book differs from other advanced calculus works ... it can serve as a useful reference for professors. ... it is the adopted course resource, its inclusion in a college library's collection should be determined by the size and interests of the mathematics faculty. Summing Up ... . Upper-division undergraduate through professional collections." (C. Bauer, Choice, Vol. 48 (8), April, 2011) "The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. ... The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. ... Strong students ... are likely to be attracted by the approach and the serious meaty content." (William J. Satzer, The Mathematical Association of America, January, 2011)
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