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Partial Differential Equations（三卷全）【Michael E. Taylor】【已搜索，无置重】
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基本信息 原书名：Partial Differential Equations(I、II、III) 原出版社： Springer 作者： Michael E. Taylor 出版社：世界图书出版公司 ISBN：9787 上架时间：2014-2-12 出版日期：2014 年1月 开本：16开 页码：1983 版次：1-1 所属分类：数学 > 分析 > 微积分 内容简介 《偏微分方程.第1卷(第2版)》这是一套3卷集经典名著，第一版曾影印出版，广受好评。第2版新增内容312页（3卷），这是第1卷。本卷在引入连续统力学、电磁学和复分析和实例的基础上，介绍了许多解决实际问题的方法，如傅里叶分析、分布理论和索伯列夫空间，这些方法可用于解决线性偏微分方程的基本问题。书中涉及的线性偏微分方程有拉普拉斯方程、热方程、波动方程、一般椭圆方程、双曲方程和抛物方程等。目次：偏微分方程和向量场基本理论；拉普拉斯方程和波动方程；傅里叶分析、分布函数和常系数线性偏微分方程；索伯列夫空间；线性椭圆方程；线性发展方程；泛函分析概述；流形、向量丛和李群。 读者对象：偏微分方程、数学物理、微分几何、调和分析和复分析等专业的研究生科研人员。 目录 《偏微分方程.第1卷(第2版)(英文影印版)》 contents of volumes ii and iii preface 1 basic theory of ode and vector fields 1 the derivative 2 fundamental local existence theorem for ode 3 inverse function and implicit function theorems 4 constant-coefficient linear systems; exponentiation of matrices 5 variable-coefficient linear systems of ode: duhamel's principle. 6 dependence of solutions on initial data and on other parameters 7 flows and vector fields 8 lie brackets 9 commuting flows; frobenius's theorem 10 hamiltonian systems 11 geodesics 12 variational problems and the stationary action principle 13 differential forms 14 the symplectic form and canonical transformations 15 first-order, scalar, nonlinear pde 16 completely integrable hamiltonian systems .17 examples of integrable systems; central force problems 18 relativistic motion 19 topological applications of differential forms 20 critical points and index of a vector field a nonsmooth vector fields references 2the laplace equation and wave equation 1 vibrating strings and membranes 2 the divergence of a vector field 3 the covariant derivative and divergence of tensor fields 4 the laplace operator on a riemannian manifold 5 the wave equation on a product manifold and energy conservation 6 uniqueness and finite propagation speed 7 lorentz manifolds and stress-energy tensors 8 more general hyperbolic equations; energy estimates 9 the symbol of a differential operator and a general green-stokes formula 10 the hodge laplacian on k-forms 11 maxwell's equations references 3fourier analysis, distributions,and constant-coefficient linear pde 1 fourier series 2 harmonic functions and holomorphic functions in the plane 3 the fourier transform 4 distributions and tempered distributions 5 the classical evolution equations 6 radial distributions, polar coordinates, and bessel functions 7 the method of images and poisson's summation formula 8 homogeneous distributions and principal value distributions 9 elliptic operators 10 local solvability of constant-coefficient pde 11 the discrete fourier transform 12 the fast fourier transform a the mighty gaussian and the sublime gamma function references 4 sobolev spaces 1 sobolev spaces on rn 2 the complex interpolation method 3 sobolev spaces on compact manifolds 4 sobolev spaces on bounded domains 5 the sobolev spaces hso (ω) 6 the schwartz kernel theorem 7 sobolev spaces on rough domains references 5linear elliptic equations 1 existence and regularity of solutions to the dirichlet problem 2 the weak and strong maximum principles 3 the dirichlet problem on the ball in rn 4 the riemann mapping theorem (smooth boundary) 5 the dirichlet problem on a domain with a rough boundary 6 the riemann mapping theorem (rough boundary) 7 the neumann boundary problem 8 the hodge decomposition and harmonic forms 9 natural boundary problems for the hodge laplacian 10 isothermal coordinates and conformal structures on surfaces 11 general elliptic boundary problems 12 operator properties of regular boundary problems a spaces of generalized functions on manifolds with boundary b the mayer-vietoris sequence in derham cohomology references 6 linear evolution equations 1 the heat equation and the wave equation on bounded domains 2 the heat equation and wave equation on unbounded domains 3 maxwell's equations 4 the cauchy-kowalewsky theorem 5 hyperbolic systems 6 geometrical optics 7 the formation of caustics 8 boundary layer phenomena for the heat semigroup a some banach spaces of harmonic functions b the stationary phase method references a outline of functional analysis 1 banach spaces 2 hilbert spaces 3 frechet spaces; locally convex spaces 4 duality 5 linear operators 6 compact operators 7 fredholm operators 8 unbounded operators 9 semigroups references b manifolds, vector bundles, and lie groups 1 metric spaces and topological spaces 2 manifolds 3 vector bundles 4 sard's theorem 5 lie groups 6 the campbell-hausdorff formula 7 representations of lie groups and lie algebras 8 representations of compact lie groups 9 representations of su(2) and related groups references index 《偏微分方程.第2卷(第2版)(英文影印版)》 contents of volumes i and iii preface pseudodifferential operators i the fourier integral representation and symbol classes 2 schwartz kernels ofpseudodifferential operators 3 adjoints and products 4 elliptic operators and parametrices 5 l2-estimates 6 garding's inequality 7 hyperbolic evolution equations 8 egorov's theorem 9 microlocal regularity 10 operators on manifolds 11 the method of layer potentials 12 parametrix for regular elliptic boundary problems 13 parametrix for the heat equation 14 the weyl calculus 15 operators of harmonic oscillator type references .8 spectral theory 1 the spectral theorem 2 self-adjoint differential operators 3 heat asymptotics and eigenvalue asymptotics 4 the laplace operator on sn 5 the laplace operator on hyperbolic space 6 the harmonic oscillator 7 the quantum coulomb problem 8 the laplace operator on cones references 9 scattering by obstacles 1 the scattering problem 2 eigenfunction expansions 3 the scattering operator 4 connections with the wave equation 5 wave operators 6 translation representations and the lax-phillips semigroup z(t) 7 integral equations and scattering poles 8 trace formulas; the scattering phase 9 scattering by a sphere 10 inverse problems i 11 inverse problems ii 12 scattering by rough obstacles a lidskii's trace theorem references 10 dirac operators and index theory 1 operators of dirac type 2 clifford algebras 3 spinors 4 weitzenbock formulas 5 index of dirac operators 6 proof of the local index formula 7 the chern-gauss-bonnet theorem 8 spinc manifolds 9 the riemann-roch theorem 10 direct attack in 2-d 11 index of operators of harmonic oscillator type references 11 brownian motion and potential theory 1 brownian motion and wiener measure 2 the feynman-kac formula 3 the diricblet problem and diffusion on domains with boundary 4 martingales, stopping times, and the strong markov property 5 first exit time and the poisson integral 6 newtonian capacity 7 stochastic integrals 8 stochastic integrals, ii 9 stochastic differential equations 10 application to equations of diffusion a the trotter product formula references 12 the -neumann problem a elliptic complexes 1 the -complex 2 morrey's inequality, the levi form, and strong pseudoconvexity 3 the 1/2-estimate and some consequences 4 higher-order subelliptic estimates 5 regularity via elliptic regularization 6 the hodge decomposition and the -equation 7 the bergman projection and toeplitz operators 8 the -neumann problem on (0, q)-forms 9 reduction to pseudodifferential equations on the boundary 10 the j-equation on complex manifolds and almost complex manifolds b complements on the levi form c the neumann operator for the dirichlet problem references c connections and curvature 1 covariant derivatives and curvature on general vector bundles 2 second covariant derivatives and covariant-exterior derivatives 3 the curvature tensor of a riemannian manifold 4 geometry of submanifoids and subbundles 5 the gauss-bonnet theorem for surfaces 6 the principal bundle picture 7 the chern-weil construction 8 the chern-gauss-bonnet theorem references index 《偏微分方程.第3卷(第2版)(英文影印版)》 contents of volumes i and ii preface 13 function space and operator theory for nonlinear analysis 1 lp-sobolev spaces 2 sobolev imbedding theorems 3 gagliardo-nirenberg-moser estimates 4 trudinger's inequalities 5 singular integral operators on lp 6 the spaces hs,p 7 lp-spectral theory of the laplace operator 8 holder spaces and zygmund spaces 9 pseudodifferential operators with nonregular symbols 10 paradifferential operators 11 young measures and fuzzy functions 12 hardy spaces a variations on complex interpolation references 14 nonlinear elliptic equations 1 a class ofsemilinear equations .2 surfaces with negative curvature 3 local solvability of nonlinear elliptic equations 4 elliptic regularity i (interior estimates) 5 isometric imbedding of riemannian manifolds 6 minimal surfaces 6b second variation of area 7 the minimal surface equation 8 elliptic regularity ii (boundary estimates) 9 elliptic regularity iii (degiorgi-nash-moser theory) 10 the dirichlet problem for quasi-linear elliptic equations 11 direct methods in the calculus of variations 12 quasi-linear elliptic systems 12b further results on quasi-linear systems 13 elliptic regularity iv (krylov-safonov estimates) 14 regularity for a class of completely nonlinear equations 15 monge-ampereequations 16 elliptic equations in two variables a morrey spaces b leray-schauder fixed-point theorems references 15 nonlinear parabolic equations 1 semilinear parabolic equations 2 applications to harmonic maps 3 semilinear equations on regions with boundary 4 reaction-diffusion equations 5 a nonlinear trotter product formula 6 the stefan problem 7 quasi-linear parabolic equations i 8 quasi-linear parabolic equations ii (sharper estimates) 9 quasi-linear parabolic equations iii (nash-moser estimates) references 16 nonlinear hyperbolic equations i quasi-linear, symmetric hyperbolic systems 2 symmetrizable hyperbolic systems 3 second-order and higher-order hyperbolic systems 4 equations in the complex domain and the cauchy-kowalewsky theorem 5 compressible fluid motion 6 weak solutions to scalar conservation laws; the viscosity method 7 systems of conservation laws in one space variable;riemann problems 8 entropy-flux pairs and riemann invariants 9 global weak solutions of some 2 x 2 systems 10 vibrating strings revisited references 17 euler and navier-stokes equations for incompressible fluids i euler's equations for ideal incompressible fluid flow 2 existence of solutions to the euler equations 3 euler flows on bounded regions 4 navier-stokes equations 5 viscous flows on bounded regions 6 vanishing viscosity limits 7 from velocity field convergence to flow convergence a regularity for the stokes system on bounded domains references 18 einstein's equations 1 the gravitational field equations 2 spherically symmetric spacetimes and the schwarzschild solution 3 stationary and static spacetimes 4 orbits in schwarzschild spacetimc 5 coupled maxwell-einstein equations 6 relativistic fluids 7 gravitational collapse 8 the initial-value problem 9 geometry of initial surfaces 10 time slices and their evolution references index 前言 Introduction to the Second Edition In addition to making numerous small corrections to this work, collected over the past dozen years, I have taken the opportunity to make some very significant changes, some of which broaden the scope of the work, some of which clarify previous presentations, and a few of which correct errors that have come to my attention. There are seven additional sections in this edition, two in Volume 1, two in Volume 2, and three in Volume 3. Chapter 4 has a new section, "Sobolev spaces on rough domains," which serves to clarify the treatment of the Dirichlet prob-lem on rough domains in Chap. 5. Chapter 6 has a new section, "Boundary layer phenomena for the beat equation," which will prove useful in one of the new sec-tions in Chap. 17. Chapter 7 has a new section, "Operators of harmonic oscillator type," and Chap. 10 has a section that presents an index formula for elliptic sys-tems of operators of harmonic oscillator type. Chapter 13 has a new appendix,"Variations on complex interpolation," which has material that is useful in the study of Zygmund spaces. Finally, Chap. 17 has two new sections, "Vanishing viscosity limits" and "From velocity convergence to flow convergence." In addition, several other sections have been substantially rewritten, and nu-merous others polished to reflect insights gained through the use of these books over time.      LZ有个小小请求，不要默默无声的下载，帮忙评论一下！多谢合作，LZ有大量电子书与大家分享！ |
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