微积分 英文 上PDF电子书下载

Chapter 1 Functions and Limits 1

1.1 Functions 1

1.2 Limits of sequence of number 10

1.3 Limit of functions 16

1.4 The operation of limits 22

1.5 The principle for existence of limits 27

1.6 Two important limist 29

1.7 Continuity of functions 34

1.8 Infinitesimal and infinity quantity,the order for infinitesimals 43

Chapter 2 Derivatives and Differentials 50

2.1 The concepts of the derivative 50

2.2 The rules of derivation 58

2.3 Higher-order derivatives and differentials of functions 66

2.4 Differential skill 71

Chapter 3 Mean Value Theorems and Applications of Derivatives 79

3.1 Mean value theorems 79

3.2 L'Hospital's rule 93

3.3 Properties of functions 98

3.4 Differentiation of arc and curvature 115

Chapter 4 Indefinite Integrals 121

4.1 Concept and properties of indefinite integral 121

4.2 Integration by substitution 127

4.3 Integration by parts 138

4.4 Integration of a several kinds of special functions 144

Chapter 5 The Definite Integral and Its Applications 155

5.1 Definition of definite integrals 155

5.2 Properties of definite integrals 161

5.3 The fundamental theorem of calculus 165

5.4 Techniques for the computation of definite integrals 171

5.5 Improper integrals 177

5.6 Applications of definite integrals 181

Chapter 6 Infinite Series 196

6.1 Series with constant terms 196

6.2 Power series 213

6.3 Taylor's series 223

6.4 Fourier series 234

6.5 Expand a function into the sine series and cosine series 244

Answers 252