Precalculus

1. TOPICS FROM ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Equations. Complex Numbers. Inequalities. 2. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. 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. Variation. 4. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. 5. TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of the Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. 6. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Additions and Subtraction of Formulas. Multiple-Angle Formulas. Product-To-Sum and Sum-To-Product Formulas. The Inverse Trigonometric Functions. 7. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre's Theorem and nth Roots of Complex Numbers. 8. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More Than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. 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. 10. TOPICS FROM ANALYTICAL GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. 11. LIMITS OF FUNCTIONS. Introductions to Limits. Definition of a Limit. Techniques for Finding Limits. Limits Involving Infinity. Appendix I: Common Graphs and Their Equations. Appendix II: A Summary of Graph Transformations. Appendix III: Graphs of the Trigonometric Functions and Their Inverses. Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle. Appendix V: Theorems on Limits.