图书介绍
数学分析原理 英文版·第3版pdf电子书版本下载
- （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：
PDF下载
下载说明
数学分析原理 英文版·第3版PDF格式电子书版下载
下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！
（文件页数 要大于 标注页数，上中下等多册电子书除外）
注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具
图书目录
Chapter 1 The Real and Complex Number Systems 1
Introduction 1
Ordered Sets 3
Fields 5
The Real Field 8
The Extended Real Number System 11
The Complex Field 12
Euclidean Spaces 16
Appendix 17
Exercises 21
Chapter 2 Basic Topology 24
Finite,Countable,and Uncountable Sets 24
Metric Spaces 30
Compact Sets 36
Perfect Sets 41
Connected Sets 42
Exercises 43
Chapter 3 Numerical Sequences and Series 47
Convergent Sequences 47
Subsequences 51
Cauchy Sequences 52
Upper and Lower Limits 55
Some Special Sequences 57
Series 58
Series of Nonnegative Terms 61
The Number e 63
The Root and Ratio Tests 65
Power Series 69
Summation by Parts 70
Absolute Convergence 71
Addition and Multiplication of Series 72
Rearrangements 75
Exercises 78
Chapter 4 Continuity 83
Limits of Functions 83
Continuous Functions 85
Continuity and Compactness 89
Continuity and Connectedness 93
Discontinuities 94
Monotonic Functions 95
Infinite Limits and Limits at Infinity 97
Exercises 98
Chapter 5 Differentiation 103
The Derivative of a Real Function 103
Mean Value Theorems 107
The Continuity of Derivatives 108
L'Hospital's Rule 109
Derivatives of Higher Order 110
Taylor's Theorem 110
Differentiation of Vector-valued Functions 111
Exercises 114
Chapter 6 The Riemann-Stieltjes Integral 120
Definition and Existence of the Integral 120
Properties of the Integral 128
Integration and Differentiation 133
Integration of Vector-valued Functions 135
Rectifiable Curves 136
Exercises 138
Chapter 7 Sequences and Series of Functions 143
Discussion of Main Problem 143
Uniform Convergence 147
Uniform Convergence and Continuity 149
Uniform Convergence and Integration 151
Uniform Convergence and Differentiation 152
Equicontinuous Families of Functions 154
The Stone-Weierstrass Theorem 159
Exercises 165
Chapter 8 Some Special Functions 172
Power Series 172
The Exponential and Logarithmic Functions 178
The Trigonometric Functions 182
The Algebraic Completeness of the Complex Field 184
Fourier Series 185
The Gamma Function 192
Exercises 196
Chapter 9 Functions of Several Variables 204
Linear Transformations 204
Differentiation 211
The Contraction Principle 220
The Inverse Function Theorem 221
The Implicit Function Theorem 223
The Rank Theorem 228
Determinants 231
Derivatives of Higher Order 235
Differentiation of Integrals 236
Exercises 239
Chapter 10 Integration of Differential Forms 245
Integration 245
Primitive Mappings 248
Partitions of Unity 251
Change of Variables 252
Differential Forms 253
Simplexes and Chains 266
Stokes'Theorem 273
Closed Forms and Exact Forms 275
Vector Analysis 280
Exercises 288
Chapter 11 The Lebesgue Theory 300
Set Functions 300
Construction of the Lebesgue Measure 302
Measure Spaces 310
Measurable Functions 310
Simple Functions 313
Integration 314
Comparison with the Riemann Integral 322
Integration of Complex Functions 325
Functions of Class ？2 325
Exercises 332
Bibliography 335
List of Special Symbols 337
Index 339