[Book Cover]

Single Variable Calculus, 2/e

Gerald L. Bradley, Claremont - McKenna College
Karl J. Smith, Santa Rosa Junior College

Published August, 1998 by Prentice Hall Engineering/Science/Mathematics

Copyright 1999, 815 pp.
Paper
ISBN 0-13-639279-2


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Summary

This text was the first written to blend much of the best aspects of calculus reform with the reasonable goals and methodology of traditional calculus. While incorporating much of calculus reform, Calculus, 2/e does not “throw the baby out with the bath water.” Calculus should not be a terminal course, but rather, one that prepares students in engineering, science, and math to move on to more advanced and necessary career or professional courses. This text addresses topics such as continuity, the mean value theorm, l'Hôpital's rule, parametric equations, polar coordinates, sequences, and series. In short, this text is an attempt at Reform with Reason. The second edition now features the total integration of transcendental functions right from the beginning of the text, as well as expanded coverage of differential equations, including slope fields in Chapter 5.

Features


NEW—Total integration of transcendental functions right from the beginning. The transcendental functions are reviewed in Chapter 1, which is now an introductory chapter. (Calculus topics begin in Chapter 2. It is possible to begin the course with Chapter 1 or Chapter 2).
NEW—Modeling was added as a major theme in this edition. In Section 2.1, modeling is introduced and then included in almost every section of the book. These applications are designated MODELING PROBLEMS.
NEW
—Differential equations are integrated into the text and coverage is expanded including an introduction to slope fields in Chapter 5.
NEW—More than 1000 new problems added to this edition.
NEW—Notes from the history of calculus are presented in the form of problems which lead the reader from the development of a concept to actually participating in the discovery process. These are designated as Historical Quest problems, which are not designed to be “add-on or challenge problems”, but they were crafted to become an integral part of the usual set of assigned problems. The level of difficulty of Quest problems ranges from easy to difficult.
NEW—A more streamlined text layout with clearer art presentation.
NEW—A calculus Website which provides animations of most text examples (including “what if” scenarios), a Net Tutor, interactive quizzes, links to other math sites, and a syllabus builder.
Student Math Handbook—this unique item is free when wrapped with every copy of the text. It contains an extensive precalculus and analytic geometry review plus table of contents.
Students benefit from innovative pedagogy and a superb range of problems.
Concepts are presented using the “Rule of Three” to reinforce and strengthen important ideas.
Qualitative and quantitative problems demonstrate an extremely wide variety of mathematical, engineering, scientific, and social models.
“What This Says” summarizes important ideas in words the students can understand. In turn, there are questions called “What Does This Say?” to encourage students to put their ideas into words.
“Journal Problems”, “Think Tank Problems”, and “Putnam Problems” require original mathematical thinking.


Table of Contents
(NOTE: Each chapter concludes with a Review and a Group Research Project or a Guest Essay.)

    1. Functions and Graphs.
    2. Limits and Continuity.
    3. Differentiation.
    4. Additional Applications of the Derivative.
    5. Integration.
    6. Additional Applications of the Integral.
    7. Methods of Integration.
    8. Infinite Series.
    9. Polar Coordinates and Parametric Forms.
    10. Vectors in the Plane and in Space.
    Appendices:
    A. Introduction to the Theory of Limits.
    B. Selected Proofs.
    C. Significant Digits.
    D. Short Table of Integrals.
    E. Answers to Selected Problems.
    Index.


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