## Table of Contents

**R. Algebra Reference**

R-1 Polynomials

R-2 Factoring

R-3 Rational Expressions

R-4 Equations

R-5 Inequalities

R-6 Exponents

R-7 Radicals

**1. Linear Functions**

1-1 Slopes and Equations of Lines

1-2 Linear Functions and Applications

1-3 The Least Squares Line

Chapter Review

Extended Application: Using Extrapolation to Predict Life Expectancy

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

2-1 Solution of Linear Systems by the Echelon Method

2-2 Solution of Linear Systems by the Gauss-Jordan Method

2-3 Addition and Subtraction of Matrices

2-4 Multiplication of Matrices

2-5 Matrix Inverses

2-6 Input-Output Models

Chapter Review

Extended Application: Contagion

**3. Linear Programming: The Graphical Method**

3-1 Graphing Linear Inequalities

3-2 Solving Linear Programming Problems Graphically

3-3 Applications of Linear Programming

Chapter Review

**4. Linear Programming: The Simplex Method**

4-1 Slack Variables and the Pivot

4-2 Maximization Problems

4-3 Minimization Problems; Duality

4-4 Nonstandard Problems

Chapter Review

Extended Application: Using Integer Programming in the Stock-Cutting Problem

**5. Mathematics of Finance**

5-1 Simple and Compound Interest

5-2 Future Value of an Annuity

5-3 Present Value of an Annuity; Amortization

Chapter Review

Extended Application: Time, Money, and Polynomials

**6. Logic**

6-1 Statements

6-2 Truth Tables and Equivalent Statements

6-3 The Conditional and Circuits

6-4 More on the Conditional

6-5 Analyzing Arguments and Proofs

6-6 Analyzing Arguments with Quantifiers

Chapter Review

Extended Application: Logic Puzzles

**7. Sets and Probability**

7-1 Sets

7-2 Applications of Venn Diagrams

7-3 Introduction to Probability

7-4 Basic Concepts of Probability

7-5 Conditional Probability; Independent Events

7-6 Bayes' Theorem

Chapter Review

Extended Application: Medical Diagnosis

**8. Counting Principles: Further Probability Topics**

8-1 The Multiplication Principle; Permutations

8-2 Combinations

8-3 Probability Applications of Counting Principles

8-4 Binomial Probability

8-5 Probability Distributions; Expected Value

Chapter Review

Extended Application: Optimal Inventory for a Service Truck

**9. Statistics**

9-1 Frequency Distributions; Measures of Central Tendency

9-2 Measures of Variation

9-3 The Normal Distribution

9-4 Normal Approximation to the Binomial Distribution

Chapter Review

Extended Application: Statistics in the Law - The Castaneda Decision

**10. Nonlinear Functions**

10-1 Properties of Functions

10-2 Quadratic Functions; Translation and Reflection

10-3 Polynomial and Rational Functions

10-4 Exponential Functions

10-5 Logarithmic Functions

10-6 Applications: Growth and Decay; Mathematics of Finance

Chapter Review

Extended Application: Characteristics of the Monkeyface Prickleback

**11. The Derivative**

11-1 Limits

11-2 Continuity

11-3 Rates of Change

11-4 Definition of the Derivative

11-5 Graphical Differentiation

Chapter Review

Extended Application: A Model for Drugs Administered Intravenously

**12. Calculating the Derivative**

12-1 Techniques for Finding Derivatives

12-2 Derivatives of Products and Quotients

12-3 The Chain Rule

12-4 Derivatives of Exponential Functions

12-5 Derivatives of Logarithmic Functions

Chapter Review

Extended Application: Electric Potential and Electric Field

**13. Graphs and the Derivative**

13-1 Increasing and Decreasing Functions

13-2 Relative Extrema

13-3 Higher Derivatives, Concavity, and the Second Derivative Test

13-4 Curve Sketching

Chapter Review

Extended Application: A Drug Concentration Model for Orally Administered

Medications (new)

**14. Applications of the Derivative**

14-1 Absolute Extrema

14-2 Applications of Extrema

14-3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand

14-4 Implicit Differentiation

14-5 Related Rates

14-6 Differentials: Linear Approximation

Chapter Review

Extended Application: A Total Cost Model for a Training Program

**15. Integration**

15-1 Antiderivatives

15-2 Substitution

15-3 Area and the Definite Integral

15-4 The Fundamental Theorem of Calculus

15-5 The Area Between Two Curves

15-6 Numerical Integration

Chapter Review

Extended Application: Estimating Depletion Dates for Minerals

**16. Further Techniques and Applications of Integration**

16-1 Integration by Parts

16-2 Volume and Average Value

16-3 Continuous Money Flow

16-4 Improper Integrals

16-5 Solutions of Elementary and Separable Differential Equations*

Chapter Review

Extended Application: Estimating Learning Curves in Manufacturing with Integrals

**17. Multivariable Calculus**

17-1 Functions of Several Variables

17-2 Partial Derivatives

17-3 Maxima and Minima

17-4 Lagrange Multipliers

17-5 Total Differentials and Approximations

17-6 Double Integrals

Chapter Review

Extended Application: Using Multivariable Fitting to Create a Response Surface Design

**18. Probability and Calculus**

18-1 Continuous Probability Models

18-2 Expected Value and Variance of Continuous Random Variables

18-3 Special Probability Density Functions

Chapter Review

Extended Application: Exponential Waiting Times

Tables

Table 1 Formulas of/from Geometry

Table 2 Area Under a Normal Curve

Table 3 Integrals

Answers to Selected Exercises

Photo Acknowledgements

Index