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.

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

Preface1. Preliminaries2. Limits3. Derivatives4. Applications of Differentiation5. Integrals6. Applications of Integration7. Inverse Functions, the Natural Logarithm, and the Exponential Function8. Techniques of Integration9. Parametric Equations and Polar Coordinates10. Infinite Series and Power SeriesAppendix. Answers to Odd-Numbered ExercisesIndex