Calculus: A Rigorous First Course

by Velleman, Daniel J.

• ISBN13: 9780486809366
• ISBN10: 0486809366
• eBook ISBN(s): 9780486818856
• Format: Paperback
• Copyright: 2017-01-18
• Publisher: Dover Publications

Summary

Designed for undergraduate mathematics majors, this rigorous and rewarding treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Author Daniel J. Velleman focuses on calculus as a tool for problem solving rather than the subject's theoretical foundations. Stressing a fundamental understanding of the concepts of calculus instead of memorized procedures, this volume teaches problem solving by reasoning, not just calculation. The goal of the text is an understanding of calculus that is deep enough to allow the student to not only find answers to problems, but also achieve certainty of the answers' correctness.
No background in calculus is necessary. Prerequisites include proficiency in basic algebra and trigonometry, and a concise review of both areas provides sufficient background. Extensive problem material appears throughout the text and includes selected answers. Complete solutions are available to instructors.

Author Biography

Daniel J. Velleman is Professor of Mathematics at Amherst College. His other books include How to Prove It: A Structured Approach.

Table of Contents

Preface

1. Preliminaries

2. Limits

3. Derivatives

4. Applications of Differentiation

5. Integrals

6. Applications of Integration

7. Inverse Functions, the Natural Logarithm, and the Exponential Function

8. Techniques of Integration

9. Parametric Equations and Polar Coordinates

10. Infinite Series and Power Series

Appendix. Answers to Odd-Numbered Exercises

Index