Brief Calculus with Applications / Edition 2

Brief Calculus with Applications / Edition 2

by Bill Armstrong, Don Davis
     
 

ISBN-10: 0130655910

ISBN-13: 9780130655912

Pub. Date: 09/28/2002

Publisher: Prentice Hall

This book, modern in its writing style as well as in its applications, contains numerous exercises—both skill oriented and applications—, real data problems, and a problem solving method. The book features exercises based on data form the World Wide Web, technology options for those who wish to use a graphing calculator, review boxes,

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Overview

This book, modern in its writing style as well as in its applications, contains numerous exercises—both skill oriented and applications—, real data problems, and a problem solving method. The book features exercises based on data form the World Wide Web, technology options for those who wish to use a graphing calculator, review boxes, strategic checkpoints, interactive activities, section summaries and projects, and chapter openers and reviews. For anyone who wants to see and understand how mathematics are used in everyday life.

Product Details

ISBN-13:
9780130655912
Publisher:
Prentice Hall
Publication date:
09/28/2002
Edition description:
2ND
Pages:
784
Product dimensions:
8.28(w) x 10.36(h) x 1.39(d)

Related Subjects

Table of Contents

1. Functions, Modeling and Average Rate of Change.
Coordinate Systems and Functions. Introduction to Problem Solving. Linear Functions and Average Rate of Change. Quadratic Functions and Average Rate of Change on an Interval. Operations on Functions. Rational, Radical and Power Functions. Exponential Functions. Logarithmic Functions. Regression and Mathematical Models (Optional Section).

2. Limits, Instantaneous Rate of Change and the Derivative.
Limits. Limits and Asymptotes. Problem Solving: Rates of Change. The Derivative. Derivatives of Constants, Powers and Sums. Derivatives of Products and Quotients. Continuity and Nondifferentiability.

3. Applications of the Derivative.
The Differential and Linear Approximations. Marginal Analysis. Measuring Rates and Errors.

4. Additional Differentiation Techniques.
The Chain Rule. Derivatives Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation and Related Rates. Elasticity of Demand.

5. Further Applications of the Derivative.
First Derivatives and Graphs. Second Derivatives and Graphs. Graphical Analysis and Curve Sketching. Optimizing Functions on a Closed Interval. The Second Derivative Test and Optimization.

6. Integral Calculus.
The Indefinite Integral. Area and the Definite Integral. Fundamental Theorem of Calculus. ProblemSolving: Integral Calculus and Total Accumulation. Integration by u-substitution. Integrals That Yield Logarithmic and Exponential Functions. Differential Equations: Separation of Variables. Differential Equations: Growth and Decay.

7. Applications of Integral Calculus.
Average Value of a Function and the Definite Integral in Finance. Area Between Curves and Applications. Economic Applications of Area between Curves. Integration by Parts. Numerical Integration. Improper Integrals.

8. Calculus of Several Variables.
Functions of Several Independent Variables. Level Curves, Contour Maps and Cross-Sectional Analysis. Partial Derivatives and Second-Order Partial Derivatives. Maxima and Minima. Lagrange Multipliers. Double Integrals.

Appendix A. Essentials of Algebra.
Appendix B. Calculator Programs.
Appendix C. Selected Proofs.

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