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
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