Elementary Calculus: An Approach Using Infinitesimals

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 limits.

Book Description

The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt. The book is now out of print and the copyright has been returned to me as the author. I have decided (as of September 2002) to make the book available for free in electronic form at this site. These PDF files were made from the printed Second Edition.

Table of Contents

• Real and Hyperreal Numbers
• Differentiation
• Continuous Functions
• Integration
• Limits, Analytic Geometry, and Approximations
• Applications of the Integral
• Trigonometric Functions
• Exponential and Logarithmic Functions
• Infinite Series
• Vectors
• Partial Differentiation
• Multiple Integrals
• Vector Calculus
• Differential Equations

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