數學分析原理（英文版第3版）（美）Walter Rudin|15475 下載 mobi epub pdf 電子書 2024

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圖書介紹

店鋪：互動齣版網圖書專營店

齣版社：機械工業齣版社

ISBN：7111133064

商品編碼：1677788873

叢書名：經典原版書庫

齣版時間：2004-01-01

頁數：342

圖書描述

書[0名0]：	數[0學0]分析原理（英文版·[0第0]3版）\|15475
圖書定價：	35元
圖書作者：	（美）Walter Rudin
齣版社：	機械工業齣版社
齣版日期：	2004/1/1 0:00:00
ISBN號：	7111133064
開本：	16開
頁數：	342
版次：	3-1

內容簡介

這是一部近代的數[0學0][0名0]著，一直受到數[0學0]界的推崇。作為Rudin的分析[0學0]經典著作之一，本書在西方各[0國0]乃至我[0國0]均有著廣泛而深遠的影響，被許多高校用做數[0學0]分析課的必選教材。本書涵蓋瞭高等微積分[0學0]的豐富內容，精彩的部分集中在基礎拓撲結構，函數項序列與級數。多變量函數以及微分形式的積分等章節。[0第0]3版經過增刪與修訂，更加符閤[0學0]生的閱讀習慣與思考方式。本書內容相[0當0]精練，結構簡單明瞭，這也是Rudin著作的一[0大0]特色。與其說這是一部教科書，不如說這是一部字典。

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

編輯推薦

這是一部近代的數[0學0][0名0]*，一直受到數[0學0]界的推崇。作為Rudin的分析[0學0]經典*作之一，本書在西方各[0國0]乃至我[0國0]均有著廣泛而深遠的影響，被許多高校用做數[0學0]分析課的必選教材。本書涵蓋瞭高等微積分[0學0]的豐富內容，*精彩的部分集中在基礎拓撲結構、函數項序列與級數、多變量函數以及微分形式的積分等章節。[0第0]3版經過增刪與修訂，*加符閤[0學0]生的閱讀習慣與思考方式。本書內容相[0當0]精練，結構簡單明瞭，這也是作者*作的一[0大0]特色。與其說這是一部教科書，不如說這是一部字典。

數學分析原理（英文版第3版）（美）Walter Rudin|15475 下載 mobi epub pdf txt 電子書格式