*PART 1 A LIBRARY OF ELEMENTARY FUNCTIONS*

** **

**1 Linear Equations and Graphs**

**1-1** Linear Equations and Inequalities

**1-2** Graphs and Lines

**1-3** Linear Regression

*Chapter 1 Review*

*Review Exercise*

* *

**2 Functions and Graphs**

**2-1** Functions

**2-2** Elementary Functions: Graphs and Transformations

**2-3** Quadratic Functions

**2-4** Exponential Functions

**2-5** Logarithmic Functions

*Chapter 2 Review*

*Review Exercise*

* *

*PART 2 FINITE MATHEMATICS*

* *

**3 Mathematics of Finance**

**3-1** Simple Interest

**3-2** Compound and Continuous Compound Interest

**3-3** Future Value of an Annuity; Sinking Funds

**3-4** Present Value of an Annuity; Amortization

*Chapter 3 Review*

*Review Exercise*

* *

**4 Systems of Linear Equations; Matrices**

**4-1** Review: Systems of Linear Equations in Two Variables

**4-2** Systems of Linear Equations and Augmented Matrices

**4-3** Gauss—Jordan Elimination

**4-4** Matrices: Basic Operations

**4-5** Inverse of a Square Matrix

**4-6** Matrix Equations and Systems of Linear Equations

**4-7** Leontief Input—Output Analysis

*Chapter 2 Review*

*Review Exercise*

* *

**5 Linear Inequalities and Linear Programming**

**5-1** Inequalities in Two Variables

**5-2** Systems of Linear Inequalities in Two Variables

**5-3** Linear Programming in Two Dimensions: A Geometric Approach

*Chapter 5 Review*

*Review Exercise*

* *

**6 Linear Programming: Simplex Method**

**6-1** A Geometric Introduction to the Simplex Method

**6-2** The Simplex Method: Maximization with Problem Constraints of the Form ≤

**6-3** The Dual Problem; Minimization with Problem Constraints of the Form ≥

**6-4** Maximization and Minimization with Mixed Problem Constraints

*Chapter 6 Review*

*Review Exercise*

* *

**7 Logic, Sets, and Counting**

**7-1** Logic

**7-2** Sets

**7-3** Basic Counting Principles

**7-4** Permutations and Combinations

*Chapter 7 Review*

*Review Exercise*

* *

**8 Probability**

**8-1** Sample Spaces, Events, and Probability

**8-2** Union, Intersection, and Complement of Events; Odds

**8-3** Conditional Probability, Intersection, and Independence

**8-4** Bayes’ Formula

**8-5** Random Variable, Probability Distribution, and Expected Value

*Chapter 8 Review*

*Review Exercise*

* *

**9 Markov Chains**

**9-1** Properties of Markov Chains

**9-2** Regular Markov Chains

**9-3** Absorbing Markov Chains

*Chapter 9 Review*

*Review Exercise*

* *

*PART 3 CALCULUS*

** **

**10 Limits and the Derivative**

**10-1** Introduction to Limits

**10-2** Continuity

**10-3** Infinite Limits and Limits at Infinity

**10-4** The Derivative

**10-5** Basic Differentiation Properties

**10-6** Differentials

**10-7** Marginal Analysis in Business and Economics

*Chapter 10 Review*

*Review Exercise*

* *

**11 Additional Derivative Topics**

**11-1** The Constant e and Continuous Compound Interest

**11-2** Derivatives of Exponential and Logarithmic Functions

**11-3** Derivatives of Products and Quotients

**11-4** The Chain Rule

**11-5** Implicit Differentiation

**11-6** Related Rates

**11-7** Elasticity of Demand

*Chapter 11 Review*

*Review Exercise*

* *

**12 Graphing and Optimization**

**12-1** First Derivative and Graphs

**12-2** Second Derivative and Graphs

**12-3** L’Hôpital’s Rule

**12-4** Curve-Sketching Techniques

**12-5** Absolute Maxima and Minima

**12-6** Optimization

*Chapter 12 Review*

*Review Exercise*

* *

**13 Integration**

**13-1** Antiderivatives and Indefinite Integrals

**13-2** Integration by Substitution

**13-3** Differential Equations; Growth and Decay

**13-4** The Definite Integral

**13-5** The Fundamental Theorem of Calculus

*Chapter 13 Review*

*Review Exercise*

* *

**14 Additional Integration Topics**

**14-1** Area between Curves

**14-2** Applications in Business and Economics

**14-3** Integration by Parts

**14-4** Integration Using Tables

*Chapter 14 Review*

*Review Exercise*

* *

**15 Multivariable Calculus**

**15-1** Functions of Several Variables

**15-2** Partial Derivatives

**15-3** Maxima and Minima

**15-4** Maxima and Minima Using Lagrange Multipliers

**15-5** Method of Least Squares

**15-6** Double Integrals over Rectangular Regions

**15-7** Double Integrals over More General Regions

*Chapter 15 Review*

*Review Exercise*

* *

**A Basic Algebra Review**

Self-Test on Basic Algebra

**A-1** Algebra and Real Numbers

**A-2** Operations on Polynomials

**A-3** Factoring Polynomials

**A-4** Operations on Rational Expressions

**A-5** Integer Exponents and Scientific Notation

**A-6** Rational Exponents and Radicals

**A-7** Quadratic Equations

**B Special Topics**

**B-1** Sequences, Series, and Summation Notation

**B-2** Arithmetic and Geometric Sequences

**B-3** The Binomial Theorem

**C Tables**

**Table I** Basic Geometric Formulas

**Table II** Integration Formulas

Answers

Index

Applications Index

A Library of Elementary Functions