This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via epsilon, delta definitions.
The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt. When the Second Edition became out of print, the copyright was returned to me as the author. In September 2002 I decided to make the book available for free in electronic form at this site. These PDF files were made from the printed Second Edition, and are continually being revised with minor corrections.
A Third Edition of this book was published by Dover Publications, Inc. in 2012, with the agreement that this online version will continue to be freely available. This gives you the choice of downloading this free version or purchasing the printed book.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
A picture of the cover
The whole book in one large file (25 megabytes)
Single chapters in much smaller files:
Preface to First and Second Editions
Contents and Introduction
Chapter 1 Real and Hyperreal Numbers
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Chapter 2 Differentiation
Chapter 3 Continuous Functions
Chapter 4 Integration
Chapter 5 Limits, Analytic Geometry, and Approximations
Chapter 6 Applications of the Integral
Chapter 7 Trigonometric Functions
Chapter 8 Exponential and Logarithmic Functions
Chapter 9 Infinite Series
Chapter 10 Vectors
Chapter 11 Partial Differentiation
Chapter 12 Multiple Integrals
Chapter 13 Vector Calculus
Chapter 14 Differential Equations
Appendix and Index
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