Two-Dimensional Calculus

by Robert Osserman, Mathematics

The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end of the book.

480 pages, Paperback

First published March 1, 1977

Reviews

[Tom Schulte · Rating 4 out of 5]

The book begins with vector basics as a natural launching point for the geometric focus. In the final chapters focusing on the double integral, this planar thinking will be especially enlightening for students nonplussed by centroids, moments, etc. Of course, the assessment of the area of a closed curve is the book’s introduction of the integral and this naturally leads to the double integral representing volume with appropriate illustrations continuing the geometric theme. This approach is comparable to that taken in An Introduction to Modern Calculus (Maak, 1963) which I feel is also worth a reprint edition. Each chapter concludes with exercises. For many of these, answers are provided in the back of the book. This is a self-contained work excellent for self-study or as an adjunct text for the undergraduate approaching this level of calculus.

[Look for my whole review to be posted at MAA Reviews: http://mathdl.maa.org/mathDL/19/]