Elementary Calculus: An Infinitesimal Approach
On-line Edition. Copyright © 2000 by H. Jerome Keisler
This is a calculus textbook at the college Freshman level ****d 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.
The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, ***er & 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.
Single chapters in much smaller files:
Preface to First and Second Editions
Contents and Introduction
Chapter 1 Real and Hyperreal Numbers
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
Epilogue
مواقع النشر (المفضلة)