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数学分析 1PDF|Epub|txt|kindle电子书版本网盘下载

数学分析 1
  • 李为民编 著
  • 出版社： 上海：上海交通大学出版社
  • ISBN：7313048882
  • 出版时间：2007
  • 标注页数：516页
  • 文件大小：94MB
  • 文件页数：40212860页
  • 主题词：数学分析－研究生－教材

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图书目录

Chapter 1 Real number system and functions1

1.1 Real number system1

1.2 Inequalities11

1.3 Functions15

Chapter 2 Sequence Limit40

2.1 Concept of sequence limit40

2.2 Properties of convergent sequences44

2.3 Fundamental theorems of sequenge limit54

2.4 Upper limit and lower limit of a sequence78

Chapter 3 Function limits and continuity91

3.1 Concept of function limits91

3.2 Properties of function limits99

3.3 Two important limits110

3.4 Infinitesimal and infinity113

3.5 Concept of continuity121

3.6 Properties of continuous functions133

3.7 Continuity of primary functions141

3.8 Uniform continuity144

Chapter 4 Derivatives and differentials168

4.1 Concept of derivatives168

4.2 Computation of derivatives183

4.3 Differentials201

4.4 Derivatives and differentials of higher order207

Chapter 5 Mean value theorems' and applications of derivative226

5.1 Mean value theorems226

5.2 Monotony and extremum of functions256

5.3 Graph of a function265

5.4 L'Hospital-rules274

5.5 Newton-Raphson method280

Chapter 6 Indefinite integrals292

6.1 Concept of indefinite integrals and fundamental formulas292

6.2 Techniques of integration298

6.3 Integration of some special kinds of functions309

Chapter 7 Definite integrals330

7.1 Concept of definite integrals330

7.2 Properties of definite integrals348

7.3 The fundamental theorems of calculus357

7.4 Integration techniques of definite integrals367

7.5 Improper integrals375

7.6 Numerical integration405

Chapter 8 Applications of definite integrals421

8.1 Applications in geometry421

8.2 Applications in physics439

Chapter 9 Preliminary of differential equations465

9.1 Basic concepts of differential equations465

9.2 Differential equations of first-order467

9.3 Degrading method of second-order differential equations482

9.4 Linear differential equations of second-order487

9.5 Second-order linear equations with constant coefficients495

9.6 Euler Equation506

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