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

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.