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  • 偏微分方程 (美)泰勒 著 文教 文轩网
  • 新华书店正版
    • 作者: (美)泰勒著
    • 出版社: 世界图书出版公司
    • 出版时间:2014-01-01 00:00:00
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    商品参数
    • 作者: (美)泰勒著
    • 出版社:世界图书出版公司
    • 出版时间:2014-01-01 00:00:00
    • 版次:1
    • 印次:1
    • 印刷时间:2014-01-01
    • 页数:614
    • 开本:24开
    • 装帧:平装
    • ISBN:9787510068140
    • 国别/地区:中国
    • 版权提供:世界图书出版公司

    偏微分方程

    作  者:(美)泰勒 著
    定  价:99
    出 版 社:世界图书出版公司
    出版日期:2014年01月01日
    页  数:614
    装  帧:平装
    ISBN:9787510068140
    主编推荐

    内容简介

    This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory graduate mathematics courses in American universities: elementary real and complex analysis, differential geometry, and measure theory.

    作者简介

    精彩内容

    目录
      Contents of Volumes I and III

    Preface

    7 Pseudo differential Operators

    1 The Fourier integral representation and symbol classes

    2 Schwartz kernels of pseudo differential 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 Wey l calculus

    15 Operators of harmonic oscillator type

    Reference




    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 equatio

    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 l

    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 Dirichlet 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 diffusio

    A The Trotter product formula

    References

    ……

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