数学专业英语PDF电子书下载

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