[Book Cover]

Brief Calculus and Its Applications, 8/e

Larry J. Goldstein, Villanova University
David C. Lay, the University of Maryland
David I. Schneider, the University of Maryland

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

Copyright 1999, 520 pp.
Cloth
ISBN 0-13-079767-7


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Summary

Once again, these extremely readable, highly regarded, and widely adopted texts present innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' “tried and true” formula — pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises — has proven to be tremendously successful with both students and instructors.

Features


NEW— Details the ways in which technology can be used to foster understanding of several topics while it facilitates computation.
NEW— Ends each chapter with a Review of Fundamental Concepts, helping students focus on the chapter's key points.
NEW— Places greater emphasis on the significance of differential equations in applications involving exponential functions.
NEW— Customized calculus software is available through the study guide.
NEW— Companion website supports and extends the materials presented in the text.
NEW— All graphs of functions have been redrawn using Mathematicia. FEATURES
Reinforces class lessons with carefully designed exercise sets, and challenges students to make their own connections.
Gets students going with practice problems that provide supported tasks.
Minimizes prerequisites, allowing those who have forgotten much of their high school mathematics to start anew with this self-contained material.
Includes many real-life applications/scenarios as well as the Index of Applications, which demonstrates to students the relevance of their studies.
Provides easy-to-understand instructions for using calculators, eliminating the need for a manual.
Makes available up-to-date, customized calculus software for instructors interested in the use of computers.
Early introduction to the derivative and its applications. (Chs. 1 & 2)


Table of Contents
(NOTE: Calculus and Its Applications, 8/E consists of Chs. 0-12. Brief Calculus and Its Applications, 8/E consists of Chs. 0-8.)

    Index of Applications.
    Preface.

    Introduction.
    0. Functions.

      Functions and Their Graphs. Some Important Functions. The Algebra of Functions. Zeros of Functions — The Quadratic Formula and Factoring. Exponents and Power Functions. Functions and Graphs in Applications.

    1. The Derivative.

      The Slope of a Straight Line. The Slope of a Curve at a Point. The Derivative. Limits and the Derivative. Differentiability and Continuity. Some Rules for Differentiation. More About Derivatives. The Derivative as a Rate of Change.

    2. Applications of the Derivative.

      Describing Graphs of Functions. The First and Second Derivative Rules. Curve Sketching (Introduction.) Curve Sketching (Conclusion.) Optimization Problems. Further Optimization Problems. Applications of Calculus to Business and Economics.

    3. Techniques of Differentiation.

      The Product and Quotient Rules. The Chain Rule and the General Power Rule. Implicit Differentiation and Related Rates.

    4. The Exponential and Natural Logarithm Functions.

      Exponential Functions. The Exponential Function egif/super_k.gifx. Differentiation of Exponential Functions. The Natural Logarithm Function. The Derivative of ln x. Properties of the Natural Logarithm Function.

    5. Applications of the Exponential and Natural Logarithm Functions.

      Exponential Growth and Decay. Compound Interest. Applications of the Natural Logarithm Function to Economics. Further Exponential Models.

    6. The Definite Integral.

      Antidifferentiation. Areas and Reimann Sums. Definite Integrals and the Fundamental Theorem. Areas in the xy-Plane. Applications of the Definite Integral.

    7. Functions of Several Variables.

      Examples of Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. Lagrange Multipliers and Constrained Optimization. The Method of Least Squares. Double Integrals.

    8. The Trigonometric Functions.

      Radian Measure of Angles. The Sine and the Cosine. Differentiation of sin t and cos t. The Tangent and Other Trigonometric Functions.

    9. Techniques of Integration.

      Integration by Substitution. Integration by Parts. Evaluation of Definite Integrals. Approximation of Definite Integrals. Some Applications of the Integral. Improper Integrals.

    10. Differential Equations.

      Solutions of Differential Equations. Separation of Variables. Numerical Solution of Differential Equations. Qualitative Theory of Differential Equations. Applications of Differential Equations.

    11. Taylor Polynomials and Infinite Series.

      Taylor Polynomials. The Newton-Raphson Algorithm. Infinite Series. Series with Positive Terms. Taylor Series.

    12. Probability and Calculus.

      Discrete Random Variables. Continuous Random Variables. Expected Value and Variance. Exponential and Normal Random Variables. Poisson and Geometric Random Variables.

    Appendices.

      A. Calculus and the TI-82 Calculator.

        B. Calculus and the TI-83 Calculator.

          C. Calculus and the TI-85 Calculator.

            D. Calculus and the TI-86 Calculator.

              E. Areas Under the Standard Normal Curve.

            Answers to Exercises.
            Index. @COURSECODE = MM0503: @COURSENAME = Applied Calculus @CGPAGE = Course Guide Page 334


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