Unit 1 Functions and Transformations

1.1 Sets

1.2 Functions

1.3 Elementary Functions

1.4 Linear Functions

1.5 Quadratic Functions

Unit 2 Differentiation

2.1 Limits

2.2 Continuity

2.3 Differentiation

2.4 Applications of Differentiation of Polynomials

2.5 Functions of Several Variables

2.6 Partial Derivatives

2.7 Applications of Partial Derivatives

Unit 3 Integration

3.1 Antidifferentiation of Functions

3.2 The Definite Integral

3.3 Double Integrals

3.4 Triple Integrals

3.5 Line Integral

Unit 4 Sequences and Series

4.1 Sequences

4.2 Series

Unit 5 Differential Equations

5.1 Linear Equations of the First Order

5.2 Linear Equations with Constant Coefficients

5.3 Linear Equations with Variable Coefficients

5.4 Linear Equations with Regular Singular Points

5.5 An Introduction to PDE

Unit 6 Algebra

6.1 Linear Equation

6.2 System of Linear Equations

6.3 Solving a Linear System

Unit 7 Geometry

7.1 Plane Geometry

7.2 Vectors and the Geometry of Space

7.3 Cylinders and Quadric Surfaces

Unit 8 Probability

8.1 Random Variables and Their Distributions

8.2 Expectation and Variance

8.3 Multivariate Distributions

8.4 The Law of Large Numbers and the Central Limit Theorem

Unit 9 Statistics

9.1 Descriptive Statistics

9.2 Sampling Distributions

9.3 Parameter estimation

9.4 Hypothesis testing

附录一 数学词汇

附录二 数学符号的读法

附录三 数学学术资源

References