Elementary Calculus: An Infinitesimal Approach (Dover Books on Mathematics) - Softcover

H. Jerome Keisler

Softcover

ISBN 10: 0486484521 ISBN 13: 9780486484525

Publisher: Dover Publications, 2012

Synopsis

This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.
Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation problems as the motivation. Later chapters develop transcendental functions, series, vectors, partial derivatives, and multiple integrals. The theory differs from traditional courses, but the notation and methods for solving practical problems are the same. The text suggests a variety of applications to both natural and social sciences.

About this title

About the Author

H. Jerome Keisler was a longtime professor at the University of Wisconsin, Madison. He pursued his Ph.D. under the direction of Alfred Tarski at the University of California, Berkeley, and his research included model theory and nonstandard analysis.

Edition details

• Publisher: Dover Publications
• Publication date: 2012
• Language: English
• ISBN 10: 0486484521
• ISBN 13: 9780486484525
• Binding: Paperback
• Edition number: 3
• Number of pages: 1008