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

By H. Jerome Keisler

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 0486484521
• ISBN13: 9780486484525
• Release Date: February 2012
• Publisher: Dover Publications
• Length: 1008 Pages
• Weight: 3.45 lbs.
• Dimensions: 2.0" x 6.8" x 9.9"

Customer Reviews

an elementary and comprehensive treatment of calculus by infinitesimals

There is a free download of this nice book at the author's website. This book is good for the elementary part of calculus from a "hyperreal" viewpoint which was first made rigorous by A.Robinson. Nevertheless, it does not cover enough "infinitesimal" multivariable calculus. E.g., it has no discussion of using Jacobians in the change of variable formula for multiple integrals. Nor does it give a treatment of Stokes' theorem etc. The interested readers many consult Luxemberg/Stroyan 1976 for a short discussion of these topics.