偏微分方程導論（第2版） 下載 mobi epub pdf 電子書 2025

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內容簡介

　　 《偏微分方程導論（第2版）》是一部數學專業研究生的偏微分方程教程。其旨在讓讀者更好地瞭解偏微分方程的經典基礎結果，為讀者更深層次學習這方麵的專著和教程提供現代理論觀點。這是第二版，較第一版增加瞭不少練習，專門增加瞭一章講述擬微分算子，增加瞭不少材料，內容更加豐富。書中的前五章講述經典理論，如一階方程，局部存在性定理，數學物理基礎偏微分方程，適時地運用現代物理技巧解釋長期研究的話題。最後三章專注於現代理論，索伯列夫空間，橢?邊界值問題和擬微分算子。

目錄

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

偏微分方程導論（第2版） 下載 mobi epub pdf txt 電子書 格式

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