1. TOPICS FROM ALGEBRA 

Real Numbers 

Exponents and Radicals 

Algebraic Expressions 

Equations 

Complex Numbers 

Inequalities 

Rectangular Coordinate Systems 

Lines 

Chapter 1 Review Exercises 

Chapter 1 Discussion Exercises 

2. FUNCTIONS 

Definition of Function 

Graphs of Functions 

Quadratic Functions 

Operations on Functions 

Inverse Functions 

Chapter 2 Review Exercises 

Chapter 2 Discussion Exercises 

3. POLYNOMIAL AND RATIONAL FUNCTIONS 

Polynomial Functions of Degree Greater than 2. Properties of Division 

Zeros of Polynomials 

Complex and Rational Zeros of Polynomials 

Rational Functions 

Chapter 3 Review Exercises 

Chapter 3 Discussion Exercises 

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS 

Exponential Functions 

The Natural Exponential Function 

Logarithmic Functions 

Properties of Logarithms 

Exponential and Logarithmic Equations 

Chapter 4 Review Exercises 

Chapter 4 Discussion Exercises 

5. THE TRIGONOMETRIC FUNCTIONS 

Angles 

Trigonometric Functions of Angles 

Trigonometric Functions of Real Numbers 

Values of the Trigonometric Functions 

Trigonometric Graphs 

Additional Trigonometric Graphs 

Applied Problems 

Chapter 5 Review Exercises 

Chapter 5 Discussion Exercises 

6. ANALYTIC TRIGONOMETRY 

Verifying Trigonometric Identities 

Trigonometric Equations 

The Addition and Subtraction Formulas 

MultipleAngle Formulas 

ProducttoSum and SumtoProduct Formulas 

The Inverse Trigonometric Functions 

Chapter 6 Review Exercises 

Chapter 6 Discussion Exercises 

7. APPLICATIONS OF TRIGONOMETRY 

The Law of Sines 

The Law of Cosines 

Trigonometric Form for Complex Numbers 

DeMoivre's Theorem and nth Roots of Complex Numbers 

Vectors 

The Dot Product 

Chapter 7 Review Exercises 

Chapter 7 Discussion Exercises 

8. SYSTEMS OF EQUATIONS AND INEQUALITIES 

Systems of Equations 

Systems of Linear Equations in Two Variables 

Systems of Linear Equations in More than Two Variables 

Partial Fractions 

Systems of Inequalities 

Linear Programming 

The Algebra of Matrices 

The Inverse of a Matrix 

Determinants 

Properties of Determinants 

Chapter 8 Review Exercises 

Chapter 8 Discussion Exercises 

9. SEQUENCES, SERIES, AND PROBABILITY 

Infinite Sequences and Summation Notation 

Arithmetic Sequences 

Geometric Sequences 

Mathematical Induction 

The Binomial Theorem 

Permutations 

Distinguishable Permutations and Combinations 

Probability 

Chapter 9 Review Exercises 

Chapter 9 Discussion Exercises 

10. TOPICS FROM ANALYTIC GEOMETRY 

Parabolas 

Ellipses 

Hyperbolas 

Plane Curves and Parametric Equations 

Polar Coordinates 

Polar Equations of Conics 

Chapter 10 Review Exercises 

Chapter 10 Discussion Exercises 

Appendix I: Using a TI82/83 Graphing Calculator 

Appendix II: Common Graphs and Their Equations 

Appendix III: A Summary of Graph Transformations 

Appendix IV: Graphs of the Trigonometric Functions and Their Inverses 

Answers to Selected Exercises 

Index of Applications 

Index 
