Principles of mathematical analysis = 数学分析原理 / 3rd ed.
副标题：无
作 者：Walter Rudin著.
分类号：O171
ISBN：9787111133063
微信扫一扫,移动浏览光盘
简介
这是一部近代的数学名著，一直受到数学界的推崇。作为Rudin的分析学经典著作之一，本书在西方各国乃至我国均有着广泛而深远的影响，被许多高校用做数学分析课的必选教材。本书涵盖了高等微积分学的丰富内容，最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。第3版经过增删与修订，更加符合学生的阅读习惯与思考方式。
本书内容相当精练，结构简单明了，这也是Rudin著作的一大特色。与其说这是一部教科书，不如说这是一部字典。
目录
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 nonnegative 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
monotonic 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 trigonometric 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
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 nonnegative 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
monotonic 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 trigonometric 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
Principles of mathematical analysis = 数学分析原理 / 3rd ed.
- 名称
- 类型
- 大小
光盘服务联系方式: 020-38250260 客服QQ：4006604884
云图客服：
用户发送的提问，这种方式就需要有位在线客服来回答用户的问题，这种 就属于对话式的,问题是这种提问是否需要用户登录才能提问
Video Player
×
Audio Player
×
pdf Player
×
