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内容简介

　　 《偏微分方程导论（第2版）》是一部数学专业研究生的偏微分方程教程。其旨在让读者更好地了解偏微分方程的经典基础结果，为读者更深层次学习这方面的专著和教程提供现代理论观点。这是第二版，较第一版增加了不少练习，专门增加了一章讲述拟微分算子，增加了不少材料，内容更加丰富。书中的前五章讲述经典理论，如一阶方程，局部存在性定理，数学物理基础偏微分方程，适时地运用现代物理技巧解释长期研究的话题。最后三章专注于现代理论，索伯列夫空间，椭?边界值问题和拟微分算子。

目录

chapter 0
preliminaries
a. notations and definitions
b. results from advanced calculus
c. convolutions
d. the fourier transform
e. distributions
f. compact operators
chapter 1
local existence theory
a. basic concepts
b. real first order equations
c. the general cauchy problem
d. the cauchy-kowalevski theorem
e. local solvability： the lewy example
f. constant-coeffcient operators： fundamental solutions

chapter 2
the laplace operator
a. symmetry properties of the laplacian
b. basic properties of harmonic functions
c. the fundamental solution
d. the dirichlet and neumann problems
e. the greens function
f. dirichlets principle
g. the dirichlet problem in a half-space
h. the dirichlet problem in a ball
i. more about harmonic functions

chapter 3
layer potentials
a. the setup
b. integral operators
c. double layer potentials
d. single layer potentials
e. solution of the problems
f. further remarks

chapter 4
the heat operator
a. the gaussian kernel
b. functions of the laplacian
c. the heat equation in bounded domains

chapter 5
the wave operator
a. the cauchy problem
b. solution of the cauchy problem
c. the inhomogeneous equation
d. fourier analysis of the wave operator
e. the wave equation in bounded domains
f. the radon transform

chapter 6
the l2 theory of derivatives
a. sobolev spaces on r
b. further results on sobolev spaces
c. local regularity of elliptic operators
d. constant-coefficient hypoelliptic operators
e. sobolev spaces on bounded domains

chapter 7
elliptic boundary value problems
a. strong ellipticity
b. on integration by parts
c. dirichlet forms and boundary conditions
d. the coercive estimate
e. existence， uniqueness， and eigenvalues
f. regularity at the boundary： the second order case
g. further results and techniques
h. epilogue： the return of the greens function

chapter 8
pseudodifferential operators
a. basic definitions and properties
b. kernels of pseudodifferential operators
c. asymptotic expansions of symbols
d. amplitudes， adjoints， and products
e. sobolev estimates
f. elliptic operators
g. introduction to microlocal analysis
h. change of coordinates
bibliography
index of symbols
index

前言/序言

偏微分方程导论（第2版） 电子书 下载 mobi epub pdf txt

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作为偏微分方程的入门书还可以

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陈省身先生推荐

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有用

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微分方程的一本经典教材了，很适合入门阅读，比起阿诺德那本有多一些的现代方法的介绍，各有千秋。

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很好的书 值得细读 必有收获

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从京东的站点到我家估计骑个电瓶车快点半个小时就到了，东西昨天早上7点到站点的，一直到今天下午4点钟左右才送到我家，怎一个服字了得，这是什么速度啊，最后几公里龟速，你前面送的再快有个毛用啊

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好好好好好好好好好好好好好好哈哈

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好

评分☆☆☆☆☆

作为偏微分方程的入门书还可以

类似图书 点击查看全场最低价