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 | |
Multiple-Angle Formulas | |
Product-to-Sum and Sum-to-Product 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 TI-82/83 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 |