Calculus: A Rigorous First Course

Book Description

Designed for undergraduate majors, this rigorous and rewarding treatment covers the usual topics of first-year : limits, derivatives, integrals, and infinite series. Author Daniel J. Velleman focuses on as a tool for problem solving rather than the subject's theoretical foundations. Stressing a fundamental understanding of the concepts of instead of memorized procedures, this volume teaches problem solving by reasoning, not just calculation. The goal of the text is an understanding of 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 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
Chapter 7 Inverse , 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

Book Details

  • Title: Calculus: A Rigorous First Course
  • Author:
  • Length: 736 pages
  • Edition: 1
  • Language: English
  • Publisher:
  • Publication Date: 2017-01-18
  • ISBN-10: 0486809366
  • ISBN-13: 9780486809366