Table of Contents
R. Review of Basic Concepts.
Real Numbers and Their Properties.
Order and Absolute Value.
Polynomials.
Factoring Polynomials.
Rational Expressions.
Rational Exponents.
Radical Expressions.
1. Equations and Inequalities.
Linear Equations.
Applications and Modeling with Linear Equations.
Complex Numbers.
Quadratic Equations.
Applications and Modeling with Quadratic Equations.
Other Types of Equations.
Inequalities.
Absolute Value Equations and Inequalities.
2. Graphs and Functions.
Graphs of Equations.
Functions.
Linear Functions.
Equations of Lines; Curve Fitting.
Graphs of Basic Functions.
Graphing Techniques.
Function Operations and Composition.
3. Polynomial and Rational Functions.
Quadratic Functions and Models.
Synthetic Division.
Zeros of Polynomial Functions.
Polynomial Functions: Graphs, Applications, and Models.
Rational Functions: Graphs, Applications, and Models.
Variation.
4. Exponential and Logarithmic Functions.
Inverse Functions.
Exponential Functions.
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.
Angles.
Trigonometric Functions.
Evaluating Trigonometric Functions.
Solving Right Triangles.
6. The Circular Functions and Their Graphs.
Radian Measure.
The Unit Circle and Circular Functions.
Graphs of the Sine and Cosine Functions.
Graphs of the Other Circular Functions.
Harmonic Motion.
7. Trigonometric Identities and Equations.
Fundamental Identities.
Verifying Trigonometric Identities.
Sum and Difference Identities.
Double-Angle Identities and Half-Angle Identities.
Inverse Circular Functions.
Trigonometric Equations.
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.
Partial Fractions.
Nonlinear Systems of Equations.
Systems of Inequalities and Linear Programming.
Properties of Matrices.
Matrix Inverses.
10. Analytic Geometry.
Parabolas.
Ellipses.
Hyperbolas.
Summary of the Conic Sections.
11. Further Topics in Algebra.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem.
Mathematical Induction.
Counting Theory.
Basics of Probability.
Appendix A. Polar Form of Conic Sections.
Appendix B. Rotation of Axes.