Preface

Acknowledgments

To the Student

Applications Index

P. Prerequisites: Fundamental Concepts of Algebra
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
P.2 Exponents and Scientific Notation
P.4 Polynomials
P.5 Factoring Polynomials
P.6 Rational Expressions

1. Equations and Inequalities
1.1 Graphs and Graphing Utilities
1.2 Linear Equations and Rational Equations
1.3 Models and Applications
1.4 Complex Numbers
1.6 Other Types of Equations
1.7 Linear Inequalities and Absolute Value Inequalities

2. Functions and Graphs
2.1 Basics of Functions and Their Graphs
2.2 More on Functions and Their Graphs
2.3 Linear Functions and Slope
2.4 More on Slope
2.5 Transformations of Functions
2.6 Combinations of Functions; Composite Functions
2.7 Inverse Functions
2.8 Distance and Midpoint Formulas; Circles

3. Polynomial and Rational Functions
3.2 Polynomial Functions and Their Graphs
3.3 Dividing Polynomials; Remainder and Factor Theorems
3.4 Zeros of Polynomial Functions
3.5 Rational Functions and Their Graphs
3.6 Polynomial and Rational Inequalities
3.7 Modeling Using Variation

4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
4.4 Exponential and Logarithmic Equations
4.5 Exponential Growth and Decay; Modeling Data

5. Trigonometric Functions
5.2 Right Triangle Trigonometry
5.3 Trigonometric Functions of Any Angle
5.4 Trigonometric Functions of Real Numbers; Periodic Functions
5.5 Graphs of Sine and Cosine Functions
5.6 Graphs of Other Trigonometric Functions
5.7 Inverse Trigonometric Functions
5.8 Applications of Trigonometric Functions

6. Analytic Trigonometry
6.1 Verifying Trigonometric Identities
6.2 Sum and Difference Formulas
6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
6.4 Product-to-Sum and Sum-to-Product Formulas
6.5 Trigonometric Equations

7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Polar Coordinates
7.4 Graphs of Polar Equations
7.5 Complex Numbers in Polar Form; DeMoivre's Theorem
7.6 Vectors
7.7 The Dot Product

8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Partial Fractions
8.4 Systems of Nonlinear Equations in Two Variables
8.5 Systems of Inequalities
8.6 Linear Programming

9. Matrices and Determinants
9.1 Matrix Solutions to Linear Systems
9.2 Inconsistent and Dependent Systems and Their Applications
9.3 Matrix Operations and Their Applications
9.4 Multiplicative Inverses of Matrices and Matrix Equations
9.5 Determinants and Cramer's Rule

10. Conic Sections and Analytic Geometry
10.1 The Ellipse
10.2 The Hyperbola
10.3 The Parabola
10.4 Rotation of Axes
10.5 Parametric Equations
10.6 Conic Sections in Polar Coordinates

11. Sequences, Induction, and Probability
11.1 Sequences and Summation Notation
11.2 Arithmetic Sequences
11.3 Geometric Sequences and Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
11.6 Counting Principles, Permutations, and Combinations
11.7 Probability

Appendix

Where Did That Come From? Selected Proofs