Calculus: A Rigorous First Course

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.

Table of Contents

Chapter 1 Preliminaries
Chapter 2 Limits
Chapter 3 Derivatives
Chapter 4 Applications Of Differentiation
Chapter 5 Integrals
Chapter 6 Applications Of Integration
Chapter 7 Inverse Functions, The Natural Logarithm, And The Exponential Function
Chapter 8 Techniques Of Integration
Chapter 9 Parametric Equations And Polar Coordinates
Chapter 10 Infinite Series And Power Series
Appendix Answers to Odd-Numbered Exercises