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数学分析原理 英文版·第3版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）鲁丁著 著
- 出版社： McGraw-Hill
- ISBN：7111133063
- 出版时间：2004
- 标注页数：342页
- 文件大小：11MB
- 文件页数：352页
- 主题词：
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图书目录
Chapter 1 The Real and Complex Number Systems1
Introduction1
Ordered Sets3
Fields5
The Real Field8
The Extended Real Number System11
The Complex Field12
Euclidean Spaces16
Appendix17
Exercises21
Chapter 2 Basic Topology24
Finite,Countable,and Uncountable Sets24
Metric Spaces30
Compact Sets36
Perfect Sets41
Connected Sets42
Exercises43
Chapter 3 Numerical Sequences and Series47
Convergent Sequences47
Subsequences51
Cauchy Sequences52
Upper and Lower Limits55
Some Special Sequences57
Series58
Series of Nonnegative Terms61
The Number e63
The Root and Ratio Tests65
Power Series69
Summation by Parts70
Absolute Convergence71
Addition and Multiplication of Series72
Rearrangements75
Exercises78
Chapter 4 Continuity83
Limits of Functions83
Continuous Functions85
Continuity and Compactness89
Continuity and Connectedness93
Discontinuities94
Monotonic Functions95
Infinite Limits and Limits at Infinity97
Exercises98
Chapter 5 Differentiation103
The Derivative of a Real Function103
Mean Value Theorems107
The Continuity of Derivatives108
L'Hospital's Rule109
Derivatives of Higher Order110
Taylor's Theorem110
Differentiation of Vector-valued Functions111
Exercises114
Chapter 6 The Riemann-Stieltjes Integral120
Definition and Existence of the Integral120
Properties of the Integral128
Integration and Differentiation133
Integration of Vector-valued Functions135
Rectifiable Curves136
Exercises138
Chapter 7 Sequences and Series of Functions143
Discussion of Main Problem143
Uniform Convergence147
Uniform Convergence and Continuity149
Uniform Convergence and Integration151
Uniform Convergence and Differentiation152
Equicontinuous Families of Functions154
The Stone-Weierstrass Theorem159
Exercises165
Chapter 8 Some Special Functions172
Power Series172
The Exponential and Logarithmic Functions178
The Trigonometric Functions182
The Algebraic Completeness of the Complex Field184
Fourier Series185
The Gamma Function192
Exercises196
Chapter 9 Functions of Several Variables204
Linear Transformations204
Differentiation211
The Contraction Principle220
The Inverse Function Theorem221
The Implicit Function Theorem223
The Rank Theorem228
Determinants231
Derivatives of Higher Order235
Differentiation of Integrals236
Exercises239
Chapter 10 Integration of Differential Forms245
Integration245
Primitive Mappings248
Partitions of Unity251
Change of Variables252
Differential Forms253
Simplexes and Chains266
Stokes'Theorem273
Closed Forms and Exact Forms275
Vector Analysis280
Exercises288
Chapter 11 The Lebesgue Theory300
Set Functions300
Construction of the Lebesgue Measure302
Measure Spaces310
Measurable Functions310
Simple Functions313
Integration314
Comparison with the Riemann Integral322
Integration of Complex Functions325
Functions of Class ？2325
Exercises332
Bibliography335
List of Special Symbols337
Index339