数学分析原理（英文版第3版）（美）Walter Rudin|15475 下载 mobi epub pdf 电子书 2024

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发表于2024-12-23

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店铺：互动出版网图书专营店

出版社：机械工业出版社

ISBN：7111133064

商品编码：1677788873

丛书名：经典原版书库

出版时间：2004-01-01

页数：342

图书描述

书[0名0]：	数[0学0]分析原理（英文版·[0第0]3版）\|15475
图书定价：	35元
图书作者：	（美）Walter Rudin
出版社：	机械工业出版社
出版日期：	2004/1/1 0:00:00
ISBN号：	7111133064
开本：	16开
页数：	342
版次：	3-1

内容简介

这是一部近代的数[0学0][0名0]著，一直受到数[0学0]界的推崇。作为Rudin的分析[0学0]经典著作之一，本书在西方各[0国0]乃至我[0国0]均有着广泛而深远的影响，被许多高校用做数[0学0]分析课的必选教材。本书涵盖了高等微积分[0学0]的丰富内容，精彩的部分集中在基础拓扑结构，函数项序列与级数。多变量函数以及微分形式的积分等章节。[0第0]3版经过增删与修订，更加符合[0学0]生的阅读习惯与思考方式。本书内容相[0当0]精练，结构简单明了，这也是Rudin著作的一[0大0]特色。与其说这是一部教科书，不如说这是一部字典。

Preface
Chapter 1 The Real and Complex Number Systems
Introduction
Ordered Sets
Fields
The Real Field
The Extended Real Number System
The Complex Field
Euclidean Spaces
Appendix
Exercises
Chapter 2 Basic Topology
Finite, Countable, and Uncountable Sets
Metric Spaces
Compact Sets
Perfect Sets
Connected Sets
Exercises
Chapter 3 Numerical Sequences and Series
Convergent Sequences
Subsequences
Cauchy Sequences
Upper and Lower Limits
Some Special Sequences
Series
Series of [0No0]nnegative Terms
The Number e
The Root and Ratio Tests
Power Series
Summation by Parts
Absolute Convergence
Addition and Multiplication of Series
Rearrangements
Exercises
Chapter 4 Continuity
Limits of Functions
Continuous Functions
Continuity and Compactness
Continuity and Connectedness
Discontinuities
Mo[0no0]tonic Functions
Infinite Limits and Limits at Infinity
Exercises
Chapter 5 Differentiation
The Derivative of a Real Function
Mean Value Theorems
The Continuity of Derivatives
L'Hospital's Rule
Derivatives of Higher Order
Taylor's Theorem
Differentiation of Vector-valued Functiond
Exercises
Chapter 6 The Riemann-Stieltjes Integral
Definition and Existence of the Integral
Properties of the Integral
Integration and Differentiation
Integration of Vector-valued Functions
Rectifiable Curves
Exercises
Chapter 7 Sequences and Series of Functions.
Discussion of Main Problem
Uniform Convergence
Uniform Convergence and Continuity
Uniform Convergence and Integration
Uniform Convergence and Differentiation
Equicontinuous Families of Functions
The Stone-Weierstrass Theorem
Exercises
Chapter 8 Some Special Functions
Power Series
The Exponential and Logarithrmic Functions
The Trigo[0no0]metric Functions
The Algebraic Completeness of the Complex Field
Fourier Series
The Gamma Function
Exercises
Chapter 9 Functions of Several Variables
Linear Transformations
Differentiation
The Contraction Principle
The Inverse Function Theorem
The Implicit Function Theorem
The Rank Theorem
Determinants
Derivatives of Higher Order
Differentiation of Integrals
Exercises
Chapter 10 Integration of Differential Forms
Integration
Primitive Mappings
Partitions of Unity
Change of Variables
Differential Forms
Simplexes and Chains
Stokes' Theorem
Closed Forms and Exact Forms
Vector Analysis
Exercises
Chapter 11 The Lebesgue Theory
Set Functions
Construction of the Lebesgue Measure
Measure Spaces
Measurable Functions
Simple Functions
Integration
Comparison with the Riemann Integral
Integration of Complex Functions
Functions of Class 2
Exercises
Bibliography
List of Special Symbols
Index

编辑推荐

这是一部近代的数[0学0][0名0]*，一直受到数[0学0]界的推崇。作为Rudin的分析[0学0]经典*作之一，本书在西方各[0国0]乃至我[0国0]均有着广泛而深远的影响，被许多高校用做数[0学0]分析课的必选教材。本书涵盖了高等微积分[0学0]的丰富内容，*精彩的部分集中在基础拓扑结构、函数项序列与级数、多变量函数以及微分形式的积分等章节。[0第0]3版经过增删与修订，*加符合[0学0]生的阅读习惯与思考方式。本书内容相[0当0]精练，结构简单明了，这也是作者*作的一[0大0]特色。与其说这是一部教科书，不如说这是一部字典。

数学分析原理（英文版第3版）（美）Walter Rudin|15475 下载 mobi epub pdf txt 电子书格式