Elementary Calculus: An Infinitesimal Approach

This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.

This book is concerned with the infinitesimal approach originally set forth by Newton and Leibnitz, using Non-standard Analysis. The author has moved the theoretical material from Chapter One to an Appendix in this edition. A new chapter on differential equations has been added and the transcendental functions have been fully integrated into the first section. This book should be of interest to first and second year undergraduate mathematics students.