Table of Contents
R. Review of Basic Concepts.
Real Numbers and Their Properties.
Order and Absolute Value.
1. Equations and Inequalities.
Applications and Modeling with Linear Equations.
Applications and Modeling with Quadratic Equations.
Other Types of Equations.
Absolute Value Equations and Inequalities.
2. Graphs and Functions.
Graphs of Equations.
Equations of Lines; Curve Fitting.
Graphs of Basic Functions.
Function Operations and Composition.
3. Polynomial and Rational Functions.
Quadratic Functions and Models.
Zeros of Polynomial Functions.
Polynomial Functions: Graphs, Applications, and Models.
Rational Functions: Graphs, Applications, and Models.
4. Exponential and Logarithmic Functions.
Evaluating Logarithms and the Change-of-Base Theorem.
Exponential and Logarithmic Equations.
Applications and Models of Exponential Growth and Decay.
5. Trigonometric Functions.
Evaluating Trigonometric Functions.
Solving Right Triangles.
6. The Circular Functions and Their Graphs.
The Unit Circle and Circular Functions.
Graphs of the Sine and Cosine Functions.
Graphs of the Other Circular Functions.
7. Trigonometric Identities and Equations.
Verifying Trigonometric Identities.
Sum and Difference Identities.
Double-Angle Identities and Half-Angle Identities.
Inverse Circular Functions.
Equations Involving Inverse Trigonometric Functions.
8. Applications of Trigonometry.
The Law of Sines.
The Law of Cosines.
Vectors, Operations, and the Dot Product.
Applications of Vectors.
Trigonometric (Polar) Form of Complex Numbers; Products and Quotients.
DeMoivre's Theorem; Powers and Roots of Complex Numbers.
Polar Equations and Graphs.
Parametric Equations, Graphs, and Applications.
9. Systems and Matrices.
Systems of Linear Equations.
Matrix Solution of Linear Systems.
Determinant Solution of Linear Systems.
Nonlinear Systems of Equations.
Systems of Inequalities and Linear Programming.
Properties of Matrices.
10. Analytic Geometry.
Summary of the Conic Sections.
11. Further Topics in Algebra.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem.
Basics of Probability.
Appendix A. Polar Form of Conic Sections.
Appendix B. Rotation of Axes.