PRECALCULUS

1. Functions
1.1 Quadratic Functions..................................................12
1.2 Function ..................................................................26
1.3 Analyzing Functions..................................................37
1.4 Piecewise Functions...................................................45
1.5 Transforming Function...............................................53
1.6 Composing Function..................................................69
1.7 Inverse Function........................................................75

2. Polynomial and Rational Functions
2.1 Polynomial Functions.................................................90
2.2 Diving Polynomials....................................................102
2.3 Real Zeros of Poly......................................................111
2.4 Fundamental Theorem of Algebra..............................117
2.5 Rational Function......................................................128
2.6 Polynomial and Rational Inequalities..........................145

3. Exponential and Logarithmic Functions
3.1 Exponential Function.................................................158
3.2 Compound Interest....................................................167
3.3 Logarithmic Function.................................................173
3.4 Properties of Logarithm.............................................184
3.5 Exp and Log Equations and Inequalities......................193
3.6 Exponential Growth and Modeling..............................206

4. Trigonometry Definition and Graphs
4.1 Angles in Radian........................................................214
4.2 Trigonometry of Right Triangles.................................228
4.3 Trigonometry of Any Angles......................................236
4.4 Trigonometry in Unit Circle........................................244
4.5 Trigonometric Graphs for Sin, Cos..............................249
4.6 Trigonometric Graphs for Others................................262

5. Trigonometry Identities
5.1 Inverse Trigonometry Function...................................272
5.2 Basic Trigonometric Identities....................................283
5.3 Verifying Trigonometric Identities..............................291
5.4 Sum and difference Identities....................................297
5.5 Double-Angle Identity...............................................304
5.6 Half-Angle and Product-Sum Identities.....................314

6. Trig Equations and Geometry Triangles
6.1 Basic Trigonometric Equations...................................324
6.2 More Trigonometric Equations...................................330
6.3 The Law of Sines.......................................................336
6.4 The Law of Cosines....................................................344
6.5 Area of Triangles.......................................................350

7. Polar coordinate and Complex number
7.1 Polar Coordinates......................................................358
7.2 Graphs of Polar Equations.........................................366
7.3 Complex Numbers and De Moivre’s Theorem..............376
7.4 Parametric Equations................................................388

8. Vector
8.1 Vector Basics.............................................................396
8.2 Vectors in Two Dimensions.........................................404
8.3 The Dot Product........................................................413
8.4 Three-Dimensional Coordinate..................................425
8.5 Vectors in Three Dimensions......................................430
8.6 The Cross Product.....................................................438

9. Conic Section
9.1 Conic Sections and Parabolas....................................448
9.2 Ellipses......................................................................454
9.3 Hyperbolas................................................................461
9.4 Transformation of Conics...........................................467
9.5 Rotation of Conics.....................................................479

10. Matrix and System of Equation
10.1 Systems of Linear Equations in Several Variables......486
10.2 Algebra of Matrices.................................................495
10.3 Inverse and Matrix Equation.....................................502
10.4 Partial Fractions......................................................510

11. Sequence and Series
11.1 Sequence and Sigma Notation.................................518
11.2 Arithmetic Sequence and Series..............................526
11.3 Geometric Sequence and Series...............................533
11.4 Applications of Sequence and Series........................542
11.5 Binomial Expansion.................................................547
11.6 Mathematical Induction...........................................556

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