Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises.

1. Functions

Application Preview: World Record Mile Runs

1.1 Real Numbers, Inequalities, and Lines

1.2 Exponents

1.3 Functions

1.4 Functions, Continued

1.5 Exponential Functions

1.6 Logarithmic Functions

I. Finite Mathematics

2. Mathematics of Finance

Application Preview: Musical Instruments as Investments

2.1 Simple Interest

2.2 Compound Interest

2.3 Annuities

2.4 Amortization

3. Systems of Equations and Matrices

Application Preview: A "Taxing" Problem

3.1 Systems of Two Linear Equations in Two Variables

3.2 Matrices and Linear Equations in Two Variables

3.3 Systems of Linear Equations and the Gauss-Jordan Method

3.4 Matrix Arithmetic

3.5 Inverse Matrices and Systems of Linear Equations

3.6 Introduction to Modeling: Leontief Models and Least Squares

4. Linear Programming

Application Preview: Managing an Investment Portfolio

4.1 Linear Inequalities

4.2 Two-Variable Linear Programming Problems

4.3 The Simplex Method for Standard Maximum Problems

4.4 Standard Minimum Problems and Duality

4.5* Nonstandard Problems: The Dual Pivot Element and the Two-Stage Method

4.6* Nonstandard Problems: Artificial Variables and the Big-M Method

* These two sections provide alternate methods for solving the same types of problems. The choice of which to cover is left to the Instructor.

5. Probability

Application Preview: The Chevalier de MerĂ©

5.1 Sets, Counting, and Venn Diagrams

5.2 Permutations and Combinations

5.3 Probability Spaces

5.4 Conditional Probability and Independence

5.5 Bayes'' Formula

5.6 Random Variables and Distributions

6. Statistics

Application Preview: Household Income

6.1 Random Samples and Data Organization

6.2 Measures of Central Tendency

6.3 Measures of Variation

6.4 Normal Distributions and Binomial Approximation

7. Markov Chains

Application Preview: Weather in Sri Lanka

7.1 States and Transitions

7.2 Regular Markov Chains

7.3 Absorbing Markov Chains

II. Calculus

8. Derivatives and Their Uses

Application Preview: Temperature, Superconductivity, and Limits

8.1 Limits and Continuity

8.2 Rates of Change, Slopes, and Derivatives

8.3 Some Differentiation Formulas

8.4 The Product and Quotient Rules

8.5 Higher-Order Derivatives

8.6 The Chain Rule and Generalized Power Rule

8.7 Nondifferentiable Functions

9. Further Applications of Derivatives

Application Preview: Stevens'' Law of Psychophysics

9.1 Graphing Using the First Derivative

9.2 Graphing Using the First and Second Derivatives

9.3 Optimization

9.4 Further Applications of Optimization

9.5 Optimizing Lot Size and Harvest Size

9.6 Implicit Differentiation and Related Rates

Cumulative Review for Chapters 1, 8-9

10. Exponential and Logarithmic Functions

Application Preview: Elasticity and Social Policy

10.1 Review of Exponential and Logarithmic Functions

10.2 Differentiation of Logarithmic and Exponential Functions

10.3 Two Applications to Economics: Related Rates and Elasticity of Demand

11. Integration and Its Applications

Application Preview: Cigarette Smoking

11.1 Antiderivatives and Indefinite Integrals

11.2 Integration Using Logarithmic and Exponential Functions

11.3 Definite Integrals and Areas

11.4 Further Applications of Definite Integrals: Average Value and Area Between Curves

11.5 Two Applications to Economics: Consumers'' Surplus and Income Distribution

11.6 Integration by Substitution

12. Integration Techniques and Differential Equations

Application Preview: Improper Integrals and Eternal Recognition

12.1 Integration by Parts

12.2 Integration Using Tables

12.3 Improper Integrals

12.4 Numerical Integration

12.5 Differential Equations

12.6 Further Applications of Differential Equations: Three Models of Growth

13. Calculus of Several Variables

Application Preview: Safe Cars, Unsafe Streets

13.1 Functions of Several Variables

13.2 Partial Derivatives

13.3 Optimizing Functions of Several Variables

13.4 Least Squares

13.5 Lagrange Multipliers and Constrained Optimization

13.6 Total Differentials and Approximate Changes

13.7 Multiple Integrals

Cumulative Review for Chapters 1, 8-13

Appendix: Normal Probabilities Using Tables

Answers to Selected Exercises

Index

Available on the Web

G. Game Theory

Application Preview: Sherlock Holmes and James Moriarty

G.1 Two-Person Games and Saddle Points

G.2 Mixed Strategies

G.3 Games and Linear Programming

Chapter L Logic

L.1 Statements and Connectives

Application Preview: Grammar, Logic, and Rhetoric

L.2 Truth Tables

Application Preview: Circuits

L.3 Implications

Application Preview: "If..., then..." as a Computer Instruction

L.4 Valid Arguments

Application Preview: Fuzzy Logic and Artificial Intelligence

L.5 Quantifiers and Euler Diagrams

Application Preview: The Dog Walking Ordinance

Chapter Projects and Essays