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[资源] Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】

此书的实体书已经由世图引进，买270，没钱买，所以特来分享！
实体书购买网站：http://product.china-pub.com/3801657#ml
基本信息

作者： (德)Herbert Amann Joachim Escher
出版社：世界图书出版公司
ISBN：9787
上架时间：2013-7-11
出版日期：2012 年9月
开本：16开
页码：1
版次：1-1
所属分类：数学 > 分析 > 数学分析
内容简介
这是一部三卷集的分析学习入门书籍，《分析.第1卷(英文影印版)》是第一卷。由于其在表述上的清晰性和现代特色，使得《分析.第1卷(英文影印版)》在众多同类图书中获得比较高的认可度，尤其是在基本概念讲述方面使得《分析.第1卷(英文影印版)》更胜一筹。《分析.第1卷(英文影印版)》在多变量和单变量的讲述方面浑然一体，没有进行刻意区分，重点强调了拓扑的基本知识，并将复分析基本观点也包括在里面。《分析.第1卷(英文影印版)》是学习分析基础教程的学生和老师的宝典。书中众多的例子，练习和补充材料使得《分析.第1卷(英文影印版)》也可以作为自学材料以及更高级学习的准备，也是物理和数学研究的基础。
目次：基本知识；集合；函数；相关和算子；自然数；可数性；群和同构；环、域和多项式；有理数；实数；复数；向量空间、仿射空间和代数；（二）收敛：序列的收敛；实序列和复序列；赋范向量空间；单调序列；有限极限；完备性；级数；绝对收敛；幂级数；（3）连续函数：连续性；拓扑基础；紧性；连通；r上的函数；指数和相关函数；（4）单变量微分：可微性；均值定理及其应用；泰勒定理；迭代程序；（5）函数序列：一致收敛；函数序列的连续性和可微性；解析函数；多项式逼近。
读者对象：数学专业的学生、老师以及数学和物理学工作者。

这是一部三卷集的分析学习入门书籍，《分析(第2卷)(英文影印版)》是第二卷。其中讲述了单变函数的积分理论、多维微积分理论、曲线理论和线性积分。继续了第一卷中的写作风格，囊括大量的基础知识超出了传统教科书所包括的范围。本书是学习分析基础教程的学生和老师的宝典。书中众多的例子，练习和补充材料使得本书也可以作为自学材料以及更高级学习的准备，也是物理和数学研究的基础。
目次：（6）单变量积分：跳跃连续函数；连续扩展；柯西-黎曼积分；积分的性质；积分技巧；和与积分；傅里叶级数；反常积分；gamma函数；(7)多变量微积分：连续线性映射；可微性；多变量微分准则；多线性映射；高阶可导；nemytskii算子和变量微积分；逆映射；隐函数；流形；切线和法向；（8）线性积分：曲线及其长度；rn上的曲线；pfaff形式；线性积分；同构函数；亚纯函数。
读者对象：数学专业的学生、老师以及数学和物理学工作者。

这是一部三卷集的分析学习入门书籍，《分析(第3卷)(英文影印版)》是第三卷。本卷致力于积分理论、全局积分理论基础的讲述。延续了前两卷的写作风格，严谨而又不失现代。为读者的进一步学习奠定了坚实的基础。本书是学习分析基础教程的学生和老师的宝典。书中众多的例子，练习和补充材料使得本书也可以作为自学材料以及更高级学习的准备，也是物理和数学研究的基础。
目次：（9）测度论基础：测度空间；测度；外部测度；可测集；勒贝格测度；（10）积分理论：可测函数；可积函数；收敛定理；勒贝格积分；n维bochner-lebesgue积分；fubini定理；卷积；替换法则；傅里叶变换；（11）流形和微分形式：子流形；多线性代数；微分形式的局部定理；向量域和微分形式；黎曼矩阵；向量分析；（12）流形上的积分：体积测度；微分形式的积分；stokes定理。
读者对象：数学专业的学生、老师以及数学和物理学工作者。
目录
《分析第1卷(英文影印版)》
preface
chapter i foundations
1 fundamentals of logic
2 sets
elementary facts
the power set
complement, intersection and union
products
families of sets
3 functions，
simple examples
composition of functions
commutative diagrams
injections, surjections and bijections
inverse functions
set valued functions
4 relations and operations
equivalence relations
order relations
.operations
5 the natural numbers
the peano axioms
the arithmetic of natural numbers
the division algorithm
the induction principle
recursive definitions
6 countability
permutations
equinumerous sets
countable sets
infinite products
7 groups and homomorphisms
groups
subgroups
cosets
homomorphisms
isomorphisms
8 rings, fields and polynomials
rings
the binomial theorem
the multinomial theorem
fields
ordered fields
formal power series
polynomials
polynomial functions
division of polynomiajs
linear factors
polynomials in several indeterminates
9 the rational numbers
the integers
the rational numbers
rational zeros of polynomials
square roots
10 the real numbers
order completeness
dedekind's construction of the real numbers
the natural order on r
the extended number line
a characterization of supremum and infimum
the archimedean property
the density of the rational numbers in r
nth roots
the density of the irrational numbers in r
intervals
11 the complex numbers
constructing the complex numbers
elementary properties
computation with complex numbers
balls in k
12 vector spaces, affine spaces and algebras
vector spaces
linear functions
vector space bases
affine spaces
affine functions
polynomial interpolation
algebras
difference operators and summation formulas
newton interpolation polynomials
chapter ii convergence
1 convergence of sequences
sequences
metric spaces
cluster points
convergence
bounded sets
uniqueness of the limit
subsequences
2 real and complex sequences
null sequences
elementary rules
the comparison test
complex sequences
3 normed vector spaces
norms
balls
bounded sets
examples
the space of bounded functions
inner product spaces
the cauchy-schwarz inequality
euclidean spaces
equivalent norms
convergence in product spaces
4 monotone sequences
bounded monotone sequences
some important limits
5 infinite limits
convergence to -t-oo
the limit superior and limit inferior
the bolzano-weierstrass theorem
6 completeness
cauchy sequences
banach spaces
cantor's construction of the real numbers
7 series
convergence of series
harmonic and geometric series
calculating with series
convergence tests
alternating series
decimal, binary and other representations of real numbers
the uncountability of r
8 absolute convergence
majorant, root and ratio tests
the exponential function
rearrangements of series
double series
cauchy products
9 power series
the radius of convergence
addition and multiplication of power series
the uniqueness of power series representations
chapter iii continuous functions
1 continuity
elementary properties and examples
sequential continuity
addition and multiplication of continuous functions
one-sided continuity
2 the fundamentals of topology
open sets
closed sets
the closure of a set
the interior of a set
the boundary of a set
the hausdorff condition
examples
a characterization of continuous functions
continuous extensions
relative topology
general topological spaces
3 compactness
covers
a characterization of compact sets
sequential compactness
continuous functions on compact spaces
the extreme value theorem
total boundedness
uniform continuity
compactness in general topological spaces
4 connectivity
definition and basic properties
connectivity in r
the generalized intermediate value theorem
path connectivity
connectivity in general topological spaces
5 functions on r
bolzano's intermediate value theorem
monotone functions
continuous monotone functions
6 the exponential and related functions
euler's formula
the real exponential function
the logarithm and power functions
the exponential function on ir
the definition of x and its consequences
the tangent and cotangent functions
the complex exponential function
polar coordinates
complex logarithms
complex powers
a further representation of the exponential function
chapter iv differentiation in one variable
1 differentiability
the derivative
linear approximation
rules for differentiation
the chain rule
inverse functions
differentiable functions
higher derivatives
one-sided differentiability
2 the mean value theorem and its applications
extrema
the mean value theorem
monotonicity and differentiability
convexity and differentiability
the inequalities of young, h61der and minkowski
the mean value theorem for vector valued functions
the second mean value theorem
l'hospital's rule
3 taylor's theorem
the landau symbol
taylor's formula
taylor polynomials and taylor series
the remainder function in the real case
polynomial interpolation
higher order difference quotients
4 iterative procedures
fixed points and contractions
the banach fixed point theorem
newton's method
chapter v sequences of functions
i uniform convergence
pointwise convergence
uniform convergence
series of functions
the weierstrass majorant criterion
2 continuity and differentiability for sequences of functions
continuity
locally uniform convergence
the banach space of bounded continuous functions
differentiability
3 analytic functions
differentiability of power series
analyticity
antiderivatives of analytic functions
the power series expansion of the logarithm
the binomial series
the identity theorem for analytic functions
4 polynomial appro~imation
banach algebras
density and separability
the stone-weierstrass theorem
trigonometric polynomials
periodic functions
the trigonometric approximation theorem
appendix introduction to mathematical logic
bibliography
index

《分析(第2卷)(英文影印版)》
foreword
chapter vi integral calculus in one variable
1 jnmp continuous functions
staircase and jump continuous functions
a characterization of jump continuous functions
the banach space of jump continuous functions
2 continuous extensions
the extension of uniformly continuous functions
bounded linear operators
the continuous extension of bounded linear operators
3 the cauchy-riemann integral
the integral of staircase functions
the integral of jump continuous functions
riemann sums
4 properties of integrals
integration of sequences of functions
the oriented integral
positivity and monotony of integrals
componentwise integration
.the first fundamental theorem of calculus
the indefinite integral
the mean value theorem for integrals
5 the technique of integration
variable substitution
integration by parts
the integrals of rational functions
6 sums and integrals
the bernoulli numbers
recursion formulas
the bernoulli polynomials
the euler-maclaurin sum formula
power sums
asymptotic equivalence
the riemann function
the trapezoid rule
7 fourier series
the l2 scalar product
approximating in the quadratic mean
orthonormal systems
integrating periodic functions
fourier coefficients
classical fourier series
bessel's inequality
complete orthonormal systems
piecewise continuously differentiable functions
uniform convergence
8 improper integrals
admissible functions
improper integrals
the integral comparison test for series
absolutely convergent integrals
the majorant criterion
9 the gamma function
euler's integral representation
the gamma function on c\ (-n)
gauss's representation formula
the reflection formula
the logarithmic convexity of the gamma function
stirling's formula
the euler beta integral
chapter vii multivariable differential calculus
1 continuous linear maps
the completeness of l(e, f)
finite-dimensional banaeh spaces
matrix representations
the exponential map
linear differential equations
oronwall's lemma
the variation of constants formula
determinants and eigenvalues
fundamental matrices
second order linear differential equations
2 differentiability
the definition
the derivative
directional derivatives
partial derivatives
the jacobi matrix
a differentiability criterion
the riesz representation theorem
the gradient
complex differentiability
3 multivariable differentiation rules
linearity
the chain rule
the product rule
the mean value theorem
the differentiability of limits of sequences of functions
necessary condition for local extrema
4 multillnear maps
continuous multilinear maps
the canonical isomorphism
symmetric multilinear maps
the derivative of multilinear maps
5 higher derivatives
definitions
higher order partial derivatives
the chain rule
taylor's formula
functions of rn variables
sufficient criterion for local extrema
6 nemytskii operators and the calculus of variations
nemytskii operators
the continuity of nemytskii operators
the differentiability of nemytskii operators
the differentiability of parameter-dependent integrals
variational problems
the euler-lagrange equation
classical mechanics
7 inverse maps
the derivative of the inverse of linear maps
the inverse function theorem
diffeomorphisms
the solvability of nonlinear systems of equations
8 implicit functions
differentiable maps on product spaces
the implicit function theorem
regular values
ordinary differential equations
separation of variables
lipschitz continuity and uniqueness
the picard-lindelsf theorem
9 msnifolds
submanifolds of rn
graphs
the regular value theorem
the immersion theorem
embeddings
local charts and parametrizations
change of charts
10 tangents and normals
the tangential in rn
the tangential space
characterization of the tangential space
differentiable maps
the differential and the gradient
normals
constrained extrema
applications of lagrange multipliers
chapter viii line integrals
1 curves and their lengths
the total variation
rectifiable paths
differentiable curves
rectifiable curves
2 curves in rn
unit tangent vectors
parametrization by arc length
oriented bases
the frenet n-frame
curvature of plane curves
identifying lines and circles
instantaneous circles along curves
the vector product
the curvature and torsion of space curves
3 pfaff forms
vector fields and pfaff forms
the canonical basis
exact forms and gradient fields
the poincare lemma
dual operators
transformation rules
modules
4 line integrals
the definition
elementary properties
the fundamental theorem of line integrals
simply connected sets
the homotopy invariance of line integrals
5 holomorphic functions
complex line integrals
holomorphism
the cauchy integral theorem
the orientation of circles
the cauchy integral formula
analytic functions
liouville's theorem
the fresnel integral
the maximum principle
harmonic functions
goursat's theorem
the weierstrass convergence theorem
6 meromorphic functions
the laurent expansion
removable singularities
isolated singularities
simple poles
the winding number
the continuity of the winding number
the generalized catchy integral theorem
the residue theorem
fourier integrals
references
index

《分析(第3卷)(英文影印版)》
foreword
chapter ix elements of measure theory
1 measurable spaces
σ-algebras
the borel σ-algebra
the second countability axiom
generating the borel σ-algebra with intervals
bases of topological spaces
the product topology
product borel σ-algebras
measurability of sections
2 measures
set functions
measure spaces
properties of measures
null sets
3 outer measures
the construction of outer measures
the lebesgue outer measure
.the lebesgue-stieltjes outer measure
hausdorff outer measures
4 measurable sets
motivation
the σ-algebra of μ*-measurable sets
lebesgue measure and hausdorff measure
metric measures
5 the lebesgue measure
the lebesgue measure space
the lebesgue measure is regular
a characterization of lebesgue measurability
images of lebesgue measurable sets
the lebesgue measure is translation invariant
a characterization of lebesgue measure
the lebesgue measure is invariant under rigid motions
the substitution rule for linear maps
sets without lebesgue measure
chapter x integration theory
1 measurable functions
simple functions and measurable functions
a measurability criterion
measurable r-valued functions
the lattice of measurable r-valued functions
pointwise limits of measurable functions
radon measures
2integrable functions
the integral of a simple function
the l1-seminorm
the bochner-lebesgue integral
the completeness of l1
elementary properties of integrals
convergence in l1
3 convergence theorems
integration of nonnegative r-valued functions
the monotone convergence theorem
fatou's lemma
integration of r-valued functions
lebesgue's dominated convergence theorem
parametrized integrals
4 lebesgue spaces
essentially bounded functions
the hslder and minkowski inequalities
lebesgue spaces are complete
lp-spaces
continuous functions with compact support
embeddings
continuous linear functionals on lp
5 the n-dimensional bochner-lebesgue integral
lebesgue measure spaces
the lebesgue integral of absolutely integrable functions
a characterization of riemann integrable functions
6 fubini's theorem
maps defined almost everywhere
cavalieri's principle
applications of cavalieri's principle
tonelli's theorem
fubini's theorem for scalar functions
fubini's theorem for vector-valued functions
minkowski's inequality for integrals
a characterization of lp(rm+n, e)
a trace theorem
7 the convolution
defining the convolution
the translation group
elementary properties of the convolution
approximations to the identity
test functions
smooth partitions of unity
convolutions of e-valued functions
distributions
linear differential operators
weak derivatives
8 the substitution rule
pulling back the lebesgue measure
the substitution rule: general case
plane polar coordinates
polar coordinates in higher dimensions
integration of rotationally symmetric functions
the substitution rule for vector-valued functions
9 the fourier transform
definition and elementary properties
the space of rapidly decreasing functions
the convolution algebra s
calculations with the fourier transform
the fourier integral theorem
convolutions and the fourier transform
fourier multiplication operators
plancherel's theorem
symmetric operators
the heisenberg uncertainty relation
chapter xi manifolds and differential forms
1 submanifolds
definitions and elementary properties
submersions
submanifolds with boundary
local charts
tangents and normals
the regular value theorem
one-dimensional manifolds
partitions of unity
2multilinear algebra
exterior products
pull backs
the volume element
the riesz isomorphism
the hodge star operator
indefinite inner products
tensors
3 the local theory of differential forms
definitions and basis representations
pull backs
the exterior derivative
the poincare lemma
tensors
4 vector fields and differential forms
vector fields
local basis representation
differential forms
local representations
coordinate transformations
the exterior derivative
closed and exact forms
contractions
orientability
tensor fields
5 riemannlan metrics
the volume element
riemannian manifolds
the hodge star
the codifferential
6 vector analysis
the riesz isomorphism
the gradient
the divergence
the laplace-beltrami operator
the curl
the lie derivative
the hodge-laplace operator
the vector product and the curl
chapter xii integration on manifolds
1 volume measure
the lebesgue (r-algebra of m
the definition of the volume measure
properties
integrability
calculation of several volumes
2integration of differential forms
integrals of m-forms
restrictions to submanifolds
the transformation theorem
fubini's theorem
calculations of several integrals
flows of vector fields
the transport theorem
3stokes's theorem
stokes's theorem for smooth manifolds
manifolds with singularities
stokes's theorem with singularities
planar domains
higher-dimensional problems
homotopy invariance and applications
gauss's law
green's formula
the classical stokes's theorem
the star operator and the coderivative
references

Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】-1

Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】-2

Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】-3

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