[Book Cover]

Applied Calculus for Business, Economics, Life Sciences and Social Sciences, 7/e

Raymond A. Barnett, (Emeritus) Merritt College
Michael R. Ziegler, Marquette University
Karl E. Byleen, Marquette University

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

Copyright 2000, 941 pp.
Cloth
ISBN 0-13-083129-8


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Summary

For one-quarter or one/two-semester, freshman/sophomore-level courses in Elements of Calculus, Elementary Calculus, Calculus for Business, and Calculus for Biology. Designed for students majoring in business, economics, social sciences, or life sciences, this mathematically correct, accessible, and student-friendly introduction to applied calculus prepares students to deal with calculus topics when they are encountered in other areas. The emphasis throughout is on computational skills, ideas, and problem solving—rather than on mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept, and general concepts and results are usually presented only after particular cases have been discussed.

Features


NEW—Group activities—Concludes each chapter with two group activities, with one actively involving technology.

  • Brings material to life for students, making the subject matter more interactive
NEW—Optional regression analysis—Contains optional examples and exercises illustrating the use of regression techniques to analyze real data. Includes both graphing calculator and spreadsheet output.
  • Relates the topics in the text to the real world and illustrates one of the basic tools of mathematical modeling.
NEW—More optional technology examples and exercises using actual data.
  • Helps students understand the use of technology within the mathematical arena.
NEW—Appendices with coverage of special topics.
  • Provides a more user-friendly guide to the material explored.
NEW—A basic algebra review—Appendix A concentrates on the essential skills necessary for success.
  • Depending on the background of the class, this material can be used as convenient reference or portions can be covered as part of the course.
NEW—Additional/revised exercises emphasizing exploration and discussion—Provides drill problems and applications to encourage exploration and verbalization of mathematical concepts, results, and processes, similar to the Explore-Discuss boxes. These are distributed among the exercise sets and are easily identified with exercise numbers in color.
  • Gives student a richer mathematical experience and increases communication skills.
Use of graphing calculators—In optional examples, exercises in technology, illustrations of applications of spreadsheets and sample computer output— A Graphing Calculator Manual is available for those who want extensive coverage of these devices.
  • Demonstrates for students real-world applications of technology in math.
Unparalleled topic selection, coverage, and organization.
  • Provides instructors with maximum flexibility. Gives students the essential mathematic tools needed to effectively pursue courses of study in business, economics, life sciences, and social sciences.
An abundance and variety of exercises—With over 5,500 carefully selected and graded problems.
  • Develops students' mechanical skills and increases depth of understanding.
Numerous examples—Contains over 370 numbered worked examples, many with lettered parts, which significantly increases the total number of worked examples. Each concept is illustrated with one or more examples, followed by a “Parallel” or “Matched” problem of the same type, with an answer near the end of the section so that students can immediately check their understanding of a concept. The steps used to solve each example are clearly delineated and done in enough detail so that students can follow the examples on their own.
  • Increases students' understanding of concepts and mechanics. Matched Problems actively involve students in the learning process.
An exceptional variety and quantity of applications—Offers exercise sets containing simplified application problems from real-world models carefully selected to reflect the important features of the application, without being overly difficult or obscuring the nature of the application.
  • Helps students develop mechanical skills and increases their depth of understanding.
Exploration and Discussion boxes in every section—Encourages students to think about a relationship or process before a result is stated or to investigate additional consequences of a development in the text.
  • Increases student involvement in the learning process and stimulates discussion, both in and out of class.
Exercises that encourage exploration and verbalization of mathematical concepts, results, and processes—These are distributed among the exercise sets and are easily identified with exercise numbers in color.
  • Gives students a richer mathematical experience and increases communication skills.
A Library of Elementary Functions—In Part I. Presents students with a library of elementary functions and encourages interpretation of mathematical ideas and processes graphically, numerically, and algebraically.
  • Provides instructor with flexibility by offering Part I as an option; it can be covered in its entirety or referred to as needed.
Limits—Rather than spend a great deal of time at the beginning of the course on this difficult topic, limit concepts are introduced as needed—e.g., Section 3-2 develops the limit properties necessary to find derivatives by the definition, Section 4-1 discuss continuity and graphs, and Section 4-4 discusses limits at infinity and infinite limits.
  • Introducing limits concepts as they occur naturally in the study of calculus makes them more relevant to students and also easier to understand.
Definite integrals—Introduced as a limit of a Riemann sums, following the more traditional development of integration and emphasizing understanding of basic concepts. Discusses approximations with various types of Riemann sums and some simple error estimation.
  • This approach gives students a sound understanding of basic concepts necessary for applications.
  • Increases interest level in mathematics for students. Ex. ___
Variety and quantity of exercises—Features over 4,800 carefully selected and graded problems divided into A, B, and C levels of difficulty in each exercise set. Many of these exercises have lettered parts which significantly increases the total number of exercises.
Chapter Review exercises and answers—The problems covered in each chapter are reviewed at the end of the chapter. Answers to most review problems are in the back of the book, keyed to appropriate sections. Answers to most other odd-numbered problems are also in the back of the book. Answers to application problems in linear systems and linear programming include both the mathematical model and the numeric answers.


Table of Contents
I. LIBRARY OF FUNCTIONS.
    1. A Beginning Library of Elementary Functions.
    2. Additional Elementary Functions.

II. CALCULUS.
    3. The Derivative.
    4. Graphing and Optimization.
    5. Additional Derivative Topics.
    6. Integration.
    7. Additional Integration.
    8. Multivariable Calculus.
    9. Differential Equations.
    10. Taylor Polynomials and Infinite Series.
    11. Probability and Calculus.
    12. Trigonometric Functions.
    Appendix A. Basic Algebra Review.
    Appendix B. Special Topics.
    Appendix C. Tables.
    Answers.
    Index.
    Library of Elementary Functions.
    Applications Index.


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