[Book Cover]

Calculus, 8/e

Dale Varberg, Hamline University
Edwin J. Purcell, (Deceased) University of Arizona
Steven E. Rigdon, Southern Illinois University, Edwardsville

Published September, 1999 by Prentice Hall Engineering/Science/Mathematics

Copyright 2000, 864 pp.
ISBN 0-13-081137-8

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For freshman/sophomore-level courses treating calculus of both one and several variables. While it covers all the material needed by students in engineering, science, and mathematics, this calculus text remains the shortest mainstream calculus book available—ideal for instructors who want a no-nonsense, concisely written text. The authors make effective use of computing technology, graphics, and applications. At least two technology projects are presented in each chapter. This popular book is accurate without being excessively rigorous and up-to-date without being faddish.


NEW—Hundreds of new problems—Includes problems on approximations, functions defined by tables, and conceptual questions.
NEW—Differential equations now integrated throughout the single variable part of the text—Euler's Method and slope fields are now covered; second order differential equations are retained in a separate chapter at the end of the text.
NEW—Better organized chapter layout—Now, Chapter 10 on infinite series precedes the chapter on numerical methods. The section on Taylor polynomials follows immediately after Taylor series. Also, Newton's method can be seen as an algorithm that usually yields a convergent sequence.
NEW—New technology projects—An additional technology project has been added to each chapter, making two total per chapter. Two have been added to Chapter 11.

  • With their placement at the end of each chapter, professors are given maximum flexibility in choosing the level of technology for their course.
NEW—Student Website free to adopters—Every example in the text that has a figure or piece of geometry is animated and contains questions about the animations. Extensive links to calculus materials on the Internet from around the world are found for each section of the text. True/false quizzes offer a verbal counterpart to the usual problem solving students undertake and drive students to actually read the text.
NEW—Functions defined as area under a curve, called accumulation functions, are emphasized.
  • The First Fundamental Theorem of Calculus can then be interpreted as saying that the rate of change in accumulated area is equal to the function being accumulated.
Short, sweet, and wonderfully traditional—This text stands alone with its simple, no-nonsense approach.
Emphasis on estimation throughout the text—As a way of avoiding or correcting mistakes.
  • Helps students recognize absurd answers and rework problems. Adds to the conceptual understanding of calculus.
Emphasis on explanation rather than on detailed proofs—Though many proofs can be found in the Appendix.
Fill-in-the-blank items entitled “Concepts Review”—Provided at the beginning of every problem set to build a strong conceptual foundation. Answers are recorded at the end of the problem set to provide immediate feedback.
  • Tests mastery of basic vocabulary, understanding of theorems, and ability to apply concepts in the simplest of settings.

Table of Contents
    1. Preliminaries.
    2. Functions and Limits.
    3. The Derivative.
    4. Applications of the Derivative.
    5. The Integral.
    6. Applications of the Integral.
    7. Transcendental Functions.
    8. Techniques of Integration.
    9. Indeterminate Forms and Improper Integrals.
    10. Infinite Series.
    11. Numerical Methods, Approximations.
    12. Conics and Polar Coordinates.
    13. Geometry in the Plane, Vectors.
    14. Geometry in Space, Vectors.
    15. The Derivative in n-Space.
    16. The Integral in n-Space.
    17. Vector Calculus.
    18. Differential Equations.
    Appendix: Mathematical Induction.
    Appendix: Proofs of Several Theorems.
    A Backward Look.
    Answers to Odd-Numbered Problems.
    Photo Credits.


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