Calculus and Its Applications, Brief Version, 12th edition

• Preface
• Prerequisite Skills Diagnostic Test

R. Functions, Graphs, and Models

• R.1 Graphs and Equations
• R.2 Functions and Models
• R.3 Finding Domain and Range
• R.4 Slope and Linear Functions
• R.5 Nonlinear Functions and Models
• R.6 Exponential and Logarithmic Functions
• R.7 Mathematical Modeling and Curve Fitting
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Average Price of a Movie Ticket

1. Differentiation

• 1.1 Limits: A Numerical and Graphical Approach
• 1.2 Algebraic Limits and Continuity
• 1.3 Average Rates of Change
• 1.4 Differentiation Using Limits and Difference Quotients
• 1.5 Leibniz Notation and the Power and Sum—Difference Rules
• 1.6 The Product and Quotient Rules
• 1.7 The Chain Rule
• 1.8 Higher-Order Derivatives
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Path of a Baseball: The Tale of the Tape

2. Exponential and Logarithmic Functions

• 2.1 Exponential and Logarithmic Functions of the Natural Base, e
• 2.2 Derivatives of Exponential (Base-e) Functions
• 2.3 Derivatives of Natural Logarithmic Functions
• 2.4 Applications: Uninhibited and Limited Growth Models
• 2.5 Applications: Exponential Decay
• 2.6 The Derivatives of a_x and log_ax
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: The Business of Motion Picture Revenue and DVD Release

3. Applications of Differentiation

• 3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
• 3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
• 3.3 Graph Sketching: Asymptotes and Rational Functions
• 3.4 Optimization: Finding Absolute Maximum and Minimum Values
• 3.5 Optimization: Business, Economics, and General Applications
• 3.6 Marginals, Differentials, and Linearization
• 3.7 Elasticity of Demand
• 3.8 Implicit Differentiation and Logarithmic Differentiation
• 3.9 Related Rates
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Maximum Sustainable Harvest

4. Integration

• 4.1 Antidifferentiation
• 4.2 Antiderivatives as Areas
• 4.3 Area and Definite Integrals
• 4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average
• 4.5 Integration Techniques: Substitution
• 4.6 Integration Techniques: Integration by Parts
• 4.7 Numerical Integration
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Business and Economics: Distribution of Wealth

5. Applications of Integration

• 5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss
• 5.2 Integrating Growth and Decay Models
• 5.3 Improper Integrals
• 5.4 Probability
• 5.5 Probability: Expected Value; the Normal Distribution
• 5.6 Volume
• 5.7 Differential Equations
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Curve Fitting and Volumes of Containers

6. Functions of Several Variables

• 6.1 Functions of Several Variables
• 6.2 Partial Derivatives
• 6.3 Maximum - Minimum Problems
• 6.4 An Application: The Least-Squares Technique
• 6.5 Constrained Optimization: Lagrange Multipliers and the Extreme-Value Theorem
• 6.6 Double Integrals
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Minimizing Employees’ Travel Time in a Building


• Cumulative Review

Appendices

• A. Review of Basic Algebra
• B. Indeterminate Forms and l’Hôpital’s Rule
• C. Regression and Microsoft Excel
• D. Areas for a Standard Normal Distribution
• E. Using Tables of Integration Formulas

Answers

Index of Applications

Index