Unit 1 Functions and Transformations 1
1.1 Sets 1
1.2 Functions 1
1.3 Elementary Functions 3
1.4 Linear Functions 5
1.5 Quadratic Functions 8
Unit 2 Differentiation 13
2.1 Limits 13
2.2 Continuity 14
2.3 Differentiation 14
2.4 Applications of Differentiation of Polynomials 20
2.5 Functions of Several Variables 26
2.6 Partial Derivatives 31
2.7 Applications of Partial Derivatives 32
Unit 3 Integration 42
3.1 Antidifferentiation of Functions 42
3.2 The Definite Integral 49
3.3 Double Integrals 58
3.4 Triple Integrals 61
3.5 Line Integral 63
Unit 4 Sequences and Series 69
4.1 Sequences 69
4.2 Series 70
Unit 5 Differential Equations 82
5.1 Linear Equations of the First Order 82
5.2 Linear Equations with Constant Coefficients 87
5.3 Linear Equations with Variable Coefficients 94
5.4 Linear Equations with Regular Singular Points 98
5.5 An Introduction to PDE 103
Unit 6 Algebra 111
6.1 Linear Equation 111
6.2 System of Linear Equations 117
6.3 Solving a Linear System 125
Unit 7 Geometry 134
7.1 Plane Geometry 134
7.2 Vectors and the Geometry of Space 141
7.3 Cylinders and Quadric Surfaces 150
Unit 8 Probability 161
8.1 Random Variables and Their Distributions 161
8.2 Expectation and Variance 167
8.3 Multivariate Distributions 169
8.4 The Law of Large Numbers and the Central Limit Theorem 176
Unit 9 Statistics 180
9.1 Descriptive Statistics 180
9.2 Sampling Distributions 180
9.3 Parameter estimation 182
9.4 Hypothesis testing 186
附录一 数学词汇 191
附录二 数学符号的读法 223
附录三 数学学术资源 226
References 231