Calculus & Its Applications, 3rd edition

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: Your Health Counts Literally

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 ax and loga x
• 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: Income Streams, Annuities, and Amortization

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: Multivariable Regression

7. Trigonometric Functions

• 7.1 Basics of Trigonometry
• 7.2 Derivatives of Trigonometric Functions
• 7.3 Integration of Trigonometric Functions
• 7.4 Inverse Trigonometric Functions and Applications
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Parametric Curves

8. Differential Equations

• 8.1 Direction Fields, Autonomous Forms, and Population Models
• 8.2 Applications: Inhibited Growth Models
• 8.3 First-Order Linear Differential Equations
• 8.4 Higher-Order Differential Equations and a Trigonometry Connection
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Visual Solutions (Direction Fields) and Numerical Solutions (Euler’s and Heun’s Methods) of Differential Equations

9. Sequences and Series

• 9.1 Arithmetic Sequences and Series
• 9.2 Geometric Sequences and Series
• 9.3 Simple and Compound Interest
• 9.4 Annuities and Amortization
• 9.5 Power Series and Linearization
• 9.6 Taylor Series and a Trigonometry Connection
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Sequences and Series on a Spreadsheet

10. Probability Distributions

• 10.1 A Review of Sets
• 10.2 Theoretical Probability
• 10.3 Discrete Probability Distributions
• 10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Experimental Probability and the Law of Large Numbers

11. Systems and Matrices (online only)

• 11.1 Systems of Linear Equations
• 11.2 Gaussian Elimination
• 11.3 Matrices and Row Operations
• 11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples
• 11.5 Matrix Multiplication, Multiplicative Identities, and Inverses
• 11.6 Determinants and Cramer's Rule
• 11.7 Systems of Linear Inequalities and Linear Programming
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Matrices, Curve Fitting, and Regression

12. Combinatorics and Probability (online only)

• 12.1 Compound Events and Odds
• 12.2 Combinatorics: The Multiplication Principle and Factorial Notation
• 12.3 Permutations and Distinguishable Arrangements
• 12.4 Combinations and the Binomial Theorem
• 12.5 Conditional Probability and the Hypergeometric Probability Distribution Model
• 12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model
• 12.7 Bayes Theorem
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: The Monte Carlo Method: Finding Probabilities Using a Random Number Generator

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