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Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】
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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】](https://muchongimg.xmcimg.com/data/bcs/2015/0612/bw159h3338525_1434110690_116.png#opennewwindow) ![Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】-1](https://muchongimg.xmcimg.com/data/bcs/2015/0612/w75h3338525_1434110691_624.png#opennewwindow) ![Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】-2](https://muchongimg.xmcimg.com/data/bcs/2015/0612/w72h3338525_1434110692_903.png#opennewwindow) ![Analysis[分析]【德】【Herbert Amann】【三卷全】【已搜索，无置重】-3](https://muchongimg.xmcimg.com/data/bcs/2015/0612/w84h3338525_1434110690_506.png#opennewwindow) LZ我会考考完了，特来发送此资源，如果觉得好，顶起不解释！   |
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