**Each chapter concludes with a Review and a Mathematical Snapshot.**

**Chapter 0 Algebra Review**

0.1 Sets of Real Numbers

0.2 Some Properties of Real Numbers

0.3 Exponents and Radicals

0.4 Operations with Algebraic Expressions

0.5 Factoring

0.6 Fractions

0.7 Linear Equations

0.8 Quadratic Equations Mathematical Snapshot

**Chapter 1 Applications of Equations and Inequalities**

1.1 Applications of Equations

1.2 Linear Inequalities

1.3 Applications of Inequalities

1.4 Absolute Value

**Chapter 2 Functions and Graphs**

2.1 Functions

2.2 Special Functions

2.3 Combinations of Functions

2.4 Inverse Functions

2.5 Graphs in Rectangular Coordinates

2.6 Symmetry

2.7 Translations and Reflection

**Chapter 3 Lines, Parabolas, and Systems**

3.1 Lines

3.2 Applications and Linear Functions

3.3 Quadratic Functions

3.4 Systems of Linear Equations

3.5 Nonlinear Systems

3.6 Applications of Systems of Equations

**Chapter 4 Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Logarithmic and Exponential Equations

**Chapter 5 Mathematics of Finance**

5.1 Compound Interest

5.2 Present Value

5.3 Annuities

5.4 Amortization of Loans

**Chapter 6 Matrix Algebra**

6.1 Matrices

6.2 Matrix Addition and Scalar Multiplication

6.3 Matrix Multiplication

6.4 Solving Systems by Reducing Matrices

6.5 Method of Reduction (continued)

6.6 Inverses

6.6 Leontief's Input-Output Analysis

**Chapter 7 Linear Programming**

7.1 Linear Inequalities in Two Variables

7.2 Linear Programming

7.3 Multiple Optimum Solutions

7.4 The Simplex Method

7.5 Degeneracy, Unbounded Solutions, and Multiple Optimum Solutions

7.6 Artificial Variables

7.7 Minimization

7.8 The Dual

**Chapter 8 Introduction to Probability**

8.1 Basic Counting Principle and Permutations

8.2 Combinations and Other Counting Principles

8.3 Sample Spaces and Events

8.4 Probability

8.5 Conditional Probability and Stochastic Processes

8.6 Independent Events

8.7 Bayes' Formula

**Chapter 9 Additional Topics in Probability**

9.1 Discrete Random Variables

9.2 The Binomial Distribution

9.3 Markov Chains

**Chapter 10 Limits and Continuity**

10.1 Limits

10.2 Limits (Continued)

10.3 Interest Compounded Continuously

10.4 Continuity

10.5 Continuity Applied to Inequalities

**Chapter 11 Differentiation**

11.1 The Derivative

11.2 Rules for Differentiation

11.3 The Derivative as a Rate of Change

11.4 Differentiability and Continuity

11.5 Product and Quotient Rules

11.6 The Chain Rule and the Power Rule

**Chapter 12 Additional Differentiation Topics**

12.1 Derivatives of Logarithmic Functions

12.2 Derivatives of Exponential Functions

12.3 Elasticity of Demand

12.4 Implicit Differentiation

12.5 Logarithmic Differentiation

12.6 Newton's Method

12.7 Higher Order Derivatives

**Chapter 13 Curve Sketching**

13.1 Relative Extrema

13.2 Absolute Extrema on a Closed Interval

13.3 Concavity

13.4 The Second Derivative Test

13.5 Asymptotes

13.6 Applied Maxima and Minima

**Chapter 14 Integration**

14.1 Differentials

14.2 The Indefinite Integral

14.3 Integration with Initial Conditions

14.4 Some Integration Formulas

14.5 Techniques of Integration

14.6 Summation

14.7 The Definite Integral

14.8 The Fundamental Theorem of Calculus

14.9 Approximate Integration

14.10 Area

14.11 Area Between Curves

14.12 Consumers' and Producers' Surplus

**Chapter 15 Further Methods and Applications of Integration**

15.1 Integration by Parts

15.2 Integration by Partial Fractions

15.3 Integration by Tables

15.4 Average Value of a Function

15.5 Differential Equations

15.6 More Applications of Differential Equations

15.7 Improper Integrals

**Chapter 16 Continuous Random Variables**

16.1 Continuous Random Variables

16.2 The Normal Distribution

16.3 The Normal Approximation to the Binomial Distribution

**Chapter 17 Multivariable Calculus**

17.1 Functions of Several Variables

17.2 Partial Derivatives

17.3 Applications of Partial Derivatives

17.4 Implicit Partial Differentiation

17.5 Higher Order Partial Derivatives

17.6 The Chain Rule

17.7 Maxima and Minima for Functions of Two Variables

17.8 Lagrange Multipliers

17.9 Lines of Regression

17.10 A Comment on Homogeneous Functions

17.11 Multiple Integrals

**Answers to Odd-Numbered Problems**

** **

**Index**