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 附錄一 數(shù)學(xué)詞匯 附錄二 數(shù)學(xué)符號的讀法 附錄三 數(shù)學(xué)學(xué)術(shù)資源 References