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內容簡介

　　《偏微分方程（第1捲）（第2版）》是一套3捲集經典名著，第一版曾影印齣版，廣受好評。第2版新增內容312頁（3捲），這是第1捲。本捲在引入連續統力學、電磁學和復分析和實例的基礎上，介紹瞭許多解決實際問題的方法，如傅裏葉分析、分布理論和索伯列夫空間，這些方法可用於解決綫性偏微分方程的基本問題。書中涉及的綫性偏微分方程有拉普拉斯方程、熱方程、波動方程、一般橢圓方程、雙麯方程和拋物方程等。目次：偏微分方程和嚮量場基本理論；拉普拉斯方程和波動方程；傅裏葉分析、分布函數和常係數綫性偏微分方程；索伯列夫空間；綫性橢圓方程；綫性發展方程；泛函分析概述；流形、嚮量叢和李群。

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目錄

Contents of Volumes II and III
Preface
1Basic 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-coefficientlinear systems; exponentiation of matrices
5 Variable-coefficientlinear systems of ODE: Duhamels principle
6 Dependence of solutions on initial data and on other parameters
7 Flows and vector fields
8 Lie brackets
9 Commuting flows; Frobeniuss theorem
10 Hamiltoniansystems
11 Geodesics
12 Variational problems and the stationary action principle
13 Differential forms N
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

2 The Laplace Equation and Wave Equation
1 Vibrating strings and membranes
2 The divergence of a vector field
3The 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 Maxwells equations
References

3 FourierAnalysisDistributions 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 ofimages and Poissons summation formula
8 Homogeneous distributions and principal value distributions
9 Elliptic operators
10 Local solvability ofconstant-coefficientPDE
11 The discrete Fourier transform
12 The fast Fourier transform
A The mighty Gaussian and the sublime gamma function
References

4 SobolevSpaces
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 H50（Ω）
6 The Schwartzkerneltheorem
7 Sobolev spaces on rough domains
References

5 Linear 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 ba
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 ofregular boundary problems
……
6 Linear Evolution Equations
A Outline of FunctionaIAnalysis
B Marufolds Vector Bundles and Lie Groups
……

前言/序言

偏微分方程（第1捲）（第2版） [Partial Differential Equations I Basic Theory] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

此用戶未填寫評價內容

評分☆☆☆☆☆

專業用的書，還好

評分☆☆☆☆☆

質量有瑕疵

評分☆☆☆☆☆

名作瞭，偏微分再沒更詳細的瞭。建議不要隨意購買，商科博士以下，數學碩士以下不該修煉此神功

評分☆☆☆☆☆

這本書很好，很值得好好讀讀

評分☆☆☆☆☆

印刷質量不錯，內容正在看

評分☆☆☆☆☆

好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書好書

評分☆☆☆☆☆

東西不錯，也比較經典，是好書。原版書籍

評分☆☆☆☆☆

偏微分方程三本書之一，印刷和包裝都算不壞。

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