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Table of Contents

(Each chapter concludes with a Summary and Review, and a Chapter Test.)

1. Functions, Graphs, and Models.

Graphs and Equations.

Functions and Models.

Finding Domain and Range.

Slope and Linear Functions.

Other Types of Functions.

Mathematical Modeling and Curve Fitting.

Extended Technology Application: The Ecological Effect of Global Warming.

2. Differentiation.

Limits and Continuity: Numerically and Graphically.

Limits Algebraically.

Average Rates of Change.

Differentiation Using Limits of Difference Quotients.

Differentiation Techniques: The Power and Sum-Difference Rules.

Instantaneous Rates of Change; Business Applications.

Differentiation Techniques: The Product and Quotient Rules.

The Chain Rule.

Higher-Order Derivatives.

Extended Technology Application: Path of a Baseball: The Tale of the Tape.

3. Applications of Differentiation.

Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs.

Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs.

Graph Sketching: Asymptotes and Rational Functions.

Using Derivatives to Find Absolute Maximum and Minimum Values.

Maximum-Minimum Problems; Business and Economic Applications.

Differentials.

Implicit Differentiation and Related Rates.

Extended Technology Application: Maximum Sustainable Harvest.

4. Exponential and Logarithmic Functions.

Exponential Functions.

Logarithmic Functions.

Applications: The Uninhibited Growth Model, dP/dt = kP.

Applications: Decay.

The Derivatives of ax and logax.

An Economics Application: Elasticity of Demand.

Extended Technology Application: The Business of Motion Picture Box-Office Revenue.

5. Integration.

Integration.

Area and Definite Integrals.

Limits of Sums and Accumulations.

Properties of Definite Integrals.

Integration Techniques: Substitution.

Integration Techniques: Integration by Parts.

Integration Techniques: Using Tables.

Extended Technology Application: Total Sales of Sherwin-Williams, Intel, Sprint, and The Gap.

6. Applications of Integration.

An Economics Application: Consumer's Surplus and Producer's Surplus.

Applications of the Models P e dt and P e dt.

Improper Integrals.

Probability.

Probability: Expected Value; The Normal Distribution.

Volume.

Differential Equations.

Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda.

7. Functions of Several Variables.

Functions of Several Variables.

Partial Derivatives.

Higher-Order Partial Derivatives.

Maximum-Minimum Problems.

An Application: The Least-Squares Technique.

Constrained Maximum and Minimum Values: Lagrange Multipliers.

Multiple Integration.

Extended Technology Application: Minimizing Employees' Travel Time in a Building.

Cumulative Review.


Appendix Review of Basic Algebra.


Tables.

Integration Formulas.

Areas for a Standard Normal Distribution.

Answers.


Index.

Get Calculus and Its Applications, 7th Edition by Marvin L. Bittinger, Indiana University Purdue University Indianapolis

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