Elementary Calculus An Infinitesimal Approach

by Keisler, H. Jerome

• ISBN13: 9780486484525
• ISBN10: 0486484521
• Edition: 3rd
• Format: Paperback
• Copyright: 2012-02-15
• Publisher: Dover Publications

Summary

This first-year calculus book is centered around the use of infinitesimals rather than the epsilon-delta approach. 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.

Author Biography

H. Jerome Keisler was a longtime professor at the University of Wisconsin, Madison. He pursued his Ph.D. under the direction of Alfred Tarski at the University of California, Berkeley, and his research included model theory and nonstandard analysis.

Table of Contents

Introduction

1. Real and Hyperreal Numbers

2. Differentiation

3. Continous Functions

4. Integration

5. Limits, Analytic Geometry, and Approximations

6. Applications of the Integral

7. Trigonometric Functions

8. Exponential and Logarithmic Functions

9. Infinite Series

10. Vectors

11. Partial Differentiation

12. Multiple Integrals

13. Vector Calculus

14. Differential Equations

Epilogue

Appendix: Tables

Answers to Selected Problems

Index