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| 1. TOPICS FROM ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Equations. Complex Numbers. Inequalities. Chapter 1 Review Exercises. Chapter 1 Discussion Exercises. 2. GRAPHS AND FUNCTIONS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. Chapter 2 Review Exercises. Chapter 2 Discussion Exercises. 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. Chapter 3 Review Exercises. Chapter 3 Discussion Exercises. 4. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter 4 Review Exercises. Chapter 4 Discussion Exercises. 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. Chapter 5 Review Exercises. Chapter 5 Discussion Exercises. 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. Chapter 6 Review Exercises. Chapter 6 Discussion Exercises. 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. Chapter 7 Review Exercises. Chapter 7 Discussion Exercises. 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. Chapter 8 Review Exercises. Chapter 8 Discussion Exercises. 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. Chapter 9 Review Exercises. Chapter 9 Discussion Exercises. 10. TOPICS FROM ANALYTICAL GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. Chapter 10 Review Exercises. Chapter 10 Discussion Exercises. |
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