Precalculus

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1. Functions and Graphs

1.1 Functions 1.2 Graphing Functions 1.3 Combinations of Functions 1.4 Transformations of Functions and Their Graphs 1.5 Inverse Functions 1.6 Modeling with Functions

2. Polynomial, Rational, and Power Functions

2.1 Quadratic Functions 2.2 Polynomial Functions 2.3 Dividing Polynomial Functions 2.4 Real Zeros of Polynomial Functions 2.5 Complex Zeroes of Polynomial Functions and the Fundamental Theorem of Algebra 2.6 Rational Functions and Their Graphs 2.7 Power Functions 2.8 Nonlinear Inequalities

3. Exponential and Logarithmic Functions

3.1 Exponential Functions 3.2 Logarithmic Functions 3.3 Properties of Logarithms 3.4 Solving Exponential and Logarithmic Equations 3.5 Modeling with Exponential and Logarithmic Functions

4. Trigonometric Functions

4.1 Radians and Degrees 4.2 The Unit Circle 4.3 Right Triangle Trigonometry 4.4 Circular Functions: Trigonometric Functions of Any Angle 4.5 Graphs of Sine and Cosine 4.6 Graphs of Other Trigonometric Functions 4.7 Inverse Trigonometric Functions 4.8 Applications of Trigonometric Functions

5. Analytic Trigonometry

5.1 Fundamental Trigonometric Identities 5.2 Verifying Trigonometric Identities 5.3 Sum and Difference Identities 5.4 Double-Angle, Half-Angle, and Product-to-Sum Identities 5.5 Solving Trigonometric Equations

6. Additional Topics in Trigonometry

6.1 The Law of Sines 6.2 The Law of Cosines 6.3 Vectors in the Plane 6.4 The Dot Product 6.5 Trigonometric Form of a Complex Number

7. Parametric Equations and Polar Coordinates

7.1 Parametric Equations 7.2 Polar Coordinates 7.3 Graphs of Polar Equations 7.4 Complex Numbers and DeMoivre's Theorem

8. Systems of Equations and Matrices

8.1 Solving Systems of Equations in Two Variables 8.2 Solving Systems of Equations in Several Variables 8.3 Matrices 8.4 Row Operations on Matrices 8.5 Multiplication, Inverses, and Determinants of Matrices 8.6 Partial Functions 8.7 Systems of Inequalities 8.8 Linear Programming and Other Applications of Matrices and Determinants

9. Conic Sections

9.1 Parabolas 9.2 Ellipses 9.3 Hyperbolas 9.4 Translations and Rotations of Conics 9.5 Polar Equations of Conics

10. Analytic Geometry in Three Dimensions

10.1 The Three-Dimensional Coordinate System 10.2 Vectors in Three Dimensions 10.3 The Cross Product 10.4 Lines and Planes in Three Dimensions

11. Sequences and Series

11.1 Sequences and Series and Sigma Notation 11.2 Arithmetic Sequences 11.3 Geometric Sequences and Series 11.4 Mathematical Induction 11.5 The Binomial Theorem 11.6 Counting Principles 11.7 Probability

12. Limits: An Introduction to Calculus

12.1 Limits 12.2 Evaluating Limits 12.3 The Tangent Line Problem 12.4 Limits at Infinity 12.5 The Area Problem

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