1. Linear Functions, Equations, and Inequalities. Real Numbers and Coordinate Systems.
Introduction to Relations and Functions.
Linear Functions.
Equations of Lines and Linear Models.
Linear Equations and Inequalities.
Applications of Linear Functions.
2. Analysis of Graphs of Functions. Graphs of Basic Functions and Relations; Symmetry.
Vertical and Horizontal Shifts of Graphs.
Stretching, Shrinking, and Reflecting Graphs.
Absolute Value Functions: Graphs, Equations, Inequalities, and Applications.
Piecewise-Defined Functions.
Operations and Composition.
3. Polynomial Functions. Complex Numbers.
Quadratic Functions and Graphs.
Quadratic Equations and Inequalities.
Further Applications of Quadratic Functions and Models.
Higher Degree Polynomial Functions and Graphs.
Topics in the Theory of Polynomial Functions (I).
Topics in the Theory of Polynomial Functions (II).
Polynomial Equations and Inequalities; Further Applications and Models.
4. Rational, Power, and Root Functions. Rational Functions and Graphs.
More on Graphs of Rational Functions.
Rational Equations, Inequalities, Applications, and Models.
Functions Defined by Powers and Roots.
Equations, Inequalities, and Applications Involving Root Functions.
5. Inverse, Exponential, and Logarithmic Functions. Inverse Functions.
Exponential Functions.
Logarithms and Their Properties.
Logarithmic Functions.
Exponential and Logarithmic Equations and Inequalities.
Applications and Modeling with Exponential and Logarithmic Functions.
6. Analytic Geometry. Circles and Parabolas.
Ellipses and Hyperbolas.
Summary of the Conic Sections.
Parametric Equations.
7. Matrices and Systems of Equations and Inequalities. Systems of Equations.
Solution of Linear Systems by the Echelon Method.
Solution of Linear Systems by Row Transformations.
Matrix Properties and Operations.
Determinants and Cramer's Rule.
Solution of Linear Systems by Matrix Inverses.
Systems of Inequalities and Linear Programming.
Partial Fractions.
8. Trigonometric Functions and Applications. Angles and Arcs
The Unit Circle
Graphs of the Sine and Cosine Functions
Graphs of the Other Circular Functions
Functions of Angles and Fundamental Identities
Evaluating Trigonometry Functions
Applications of Right Triangles
Harmonic Motion
9. Trigonometric Identities and Equations. Identities.
Further Identities.
The Inverse Circular Functions.
Trigonometric Equations and Inequalities.
Further Equations and Inequalities.
10. Applications of Trigonometry; Vectors. The Law of Sines.
The Law of Cosines and Area Formulas.
Vectors and Their Applications.
Trigonometric (Polar) Form of Complex Numbers.
Powers and Roots of Complex Numbers.
Polar Equations, Graphs, and Applications.
More Parametric Equations.
11. Further Topics in Algebra. Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem.
Mathematical Induction.
Counting Theory.
Probability.
12. An Introduction to Calculus: Limits and Derivatives. An Introduction to Limits.
Techniques for Calculating Limits.
One-Sided Limits; Limits Involving Infinity.
Tangent Lines and Derivatives.
Area Under a Curve.
R. Reference: Basic Algebraic Concepts and Geometry Formulas. Review of Exponents and Polynomials.
Review of Factoring.
Review of Rational Expressions.
Review of Negative and Rational Exponents.
Review of Radicals.
Review of Geometry Formulas.
Appendix A. Vectors in Space. Appendix B. Polar Form of Conic Sections. Appendix C. Rotation of Axes. 