## Table of Contents

**1. Algebra and Equations**

1.1 The Real Numbers

1.2 Polynomials

1.3 Factoring

1.4 Rational Expressions

1.5 Exponents and Radicals

1.6 First-Degree Equations

1.7 Quadratic Equations

Summary and Review

Case Study 1 Consumers Often Need to Just Do the Math

**2. Graphs, Lines, and Inequalities**

2.1 Graphs

2.2 Equations of Lines

2.3 Linear Models

2.4 Linear Inequalities

2.5 Polynomial and Rational Inequalities

Summary and Review

Case Study 2 Using Extrapolation and Interpolation for Prediction

**3. Functions and Graphs**

3.1 Functions

3.2 Graphs of Functions

3.3 Applications of Linear Functions

3.4 Quadratic Functions and Applications

3.5 Polynomial Functions

3.6 Rational Functions

Summary and Review

Case Study 3 Architectural Arches

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Applications of Exponential Functions

4.3 Logarithmic Functions

4.4 Logarithmic and Exponential Equations

Summary and Review

Case Study 4 Gapminder.org

**5. Mathematics of Finance**

5.1 Simple Interest and Discount

5.2 Compound Interest

5.3 Annuities, Future Value, and Sinking Funds

5.4 Annuities, Present Value, and Amortization

Summary and Review

Case Study 5 Continuous Compounding

**6. Systems of Linear Equations and Matrices**

6.1 Systems of Two Linear Equations in Two Variables

6.2 Larger Systems of Linear Equations

6.3 Applications of Systems of Linear Equations

6.4 Basic Matrix Operations

6.5 Matrix Products and Inverses

6.6 Applications of Matrices

Summary and Review

Case Study 6 Matrix Operations and Airline Route Maps

**7. Linear Programming**

7.1 Graphing Linear Inequalities in two Variables

7.2 Linear Programming: The Graphical Method

7.3 Applications of Linear Programming

7.4 The Simplex Method: Maximization

7.5 Maximization Applications

7.6 The Simplex Method: Duality and Minimization

7.7 The Simplex Method: Nonstandard Problems

Summary and Review

Case Study 7 Cooking with Linear Programming

**8. Sets and Probability**

8.1 Sets

8.2 Applications of Venn Diagrams and Contingency Tables

8.3 Introduction to Probability

8.4 Basic Concepts of Probability

8.5 Conditional Probability and Independent Events

8.6 Bayes' Formula

Summary and Review

Case Study 8 Medical Diagnosis

**9. Counting, Probability Distributions, and Further Topics in Probability**

9.1 Probability Distributions and Expected Value

9.2 The Multiplication Principle, Permutations, and Combinations

9.3 Applications of Counting

9.4 Binomial Probability

9.5 Markov Chains

9.6 Decision Making

Summary and Review

Case Study 9 Quick Draw®from the New York State Lottery

**10. Introduction to Statistics**

10.1 Frequency Distributions

10.2 Measures of Center

10.3 Measures of Variation

10.4 Normal Distributions and Boxplots

10.5 Normal Approximation to the Binomial Distribution

Summary and Review

Case Study 10 Standard Deviation as a Measure of Risk

**11. Differential Calculus**

11.1 Limits

11.2 One-sided Limits and Limits Involving Infinity

11.3 Rates of Change

11.4 Tangent Lines and Derivatives

11.5 Techniques for Finding Derivatives

11.6 Derivatives of Products and Quotients

11.7 The Chain Rule

11.8 Derivatives of Exponential and Logarithmic Functions

11.9 Continuity and Differentiability

Summary and Review

Case Study 11 Price Elasticity

**12. Applications of the Derivative**

12.1 Derivatives and Graphs

12.2 The Second Derivative

12.3 Optimization Applications

12.4 Implicit Differentiation

12.5 Related Rates

12.6 Curve Sketching

Summary and Review

Case Study 12 A Total Cost Model for a Training Program

**13. Integral Calculus**

13.1 Antiderivatives

13.2 Integration by Substitution

13.3 Area and the Definite Integral

13.4 The Fundamental Theorem of Calculus

13.5 Applications of Integrals

13.6 Tables of Integrals (Optional)

13.7 Differential Equations

Summary and Review

Case Study 13 Bounded Population Growth

**14. Multivariate Calculus**

14.1 Functions of Several Variables

14.2 Partial Derivatives

14.3 Extrema of Functions of Several Variables

14.4 Lagrange Multipliers

Summary and Review

Case Study 14 Global Warming and the Method of Least Squares

**Appendices**

Appendix A. Graphing Calculators

Appendix B: Tables

Table 1: Formulas from Geometry

Table 2: Areas under the Normal Curve

Table 3: Integrals

Appendix C. Learning Objectives

Appendix D. Solutions to Prerequisite Skills Tests

Answers to Selected Exercises

Index of Companies, Products, and Agencies

Index of Applications

Subject Index