偏微分方程（第1卷）（第2版）

图书标准信息

• 作者 [美]泰勒（Taylor M.E.） 著
• 出版社 世界图书出版公司
• 出版时间 2014-01
• 版次 3
• ISBN 9787510068133
• 定价 99.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 654页
• 正文语种 英语

【内容简介】

　　《偏微分方程（第1卷）（第2版）》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。

【目录】

ContentsofVolumesIIandIII
Preface
1BasicTheoryofODEandVectorFields
1Thederivative
2FundamentallocalexistencetheoremforODE
3Inversefunctionandimplicitfunctiontheorems
4Constant-coefficientlinearsystems;exponentiationofmatrices
5Variable-coefficientlinearsystemsofODE:Duhamelsprinciple
6Dependenceofsolutionsoninitialdataandonotherparameters
7Flowsandvectorfields
8Liebrackets
9Commutingflows;Frobeniusstheorem
10Hamiltoniansystems
11Geodesics
12Variationalproblemsandthestationaryactionprinciple
13DifferentialformsN
14Thesymplecticformandcanonicaltransformations
15First-orderscalarnonlinearPDE
16Completelyintegrablehamiltoniansystems
17Examplesofintegrablesystems;centralforceproblems
18Relativisticmotion
19Topologicalapplicationsofdifferentialforms
20Criticalpointsandindexofavectorfield
ANonsmoothvectorfields
References

2TheLaplaceEquationandWaveEquation
1Vibratingstringsandmembranes
2Thedivergenceofavectorfield
3Thecovariantderivativeanddivergenceoftensorfields
4TheLaplaceoperatoronaRiemannianmanifold
5Thewaveequationonaproductmanifoldandenergyconservation
6Uniquenessandfinitepropagationspeed
7Lorentzmanifoldsandstress-energytensors
8Moregeneralhyperbolicequations;energyestimates
9ThesymbolofadifferentialoperatorandageneralGreen-Stokesformula
10TheHodgeLaplacianonk-forms
11Maxwellsequations
References

3FourierAnalysisDistributionsandConstant-CoefficientLinearPDE
1Fourierseries
2Harmonicfunctionsandholomorphicfunctionsintheplane
3TheFouriertransform
4Distributionsandtempereddistributions
5Theclassicalevolutionequations
6RadialdistributionspolarcoordinatesandBesselfunctions
7ThemethodofimagesandPoissonssummationformula
8Homogeneousdistributionsandprincipalvaluedistributions
9Ellipticoperators
10Localsolvabilityofconstant-coefficientPDE
11ThediscreteFouriertransform
12ThefastFouriertransform
AThemightyGaussianandthesublimegammafunction
References

4SobolevSpaces
1SobolevspacesonRn
2Thecomplexinterpolationmethod
3Sobolevspacesoncompactmanifolds
4Sobolevspacesonboundeddomains
5TheSobolevspacesH50（Ω）
6TheSchwartzkerneltheorem
7Sobolevspacesonroughdomains
References

5LinearEllipticEquations
1ExistenceandregularityofsolutionstotheDirichletproblem
2Theweakandstrongmaximumprinciples
3TheDirichletproblemontheba
4TheRiemannmappingtheorem（smoothboundary）
5TheDirichletproblemonadomainwitharoughboundary
6TheRiemannmappingtheorem（roughboundary）
7TheNeumannboundaryproblem
8TheHodgedecompositionandharmonicforms
9NaturalboundaryproblemsfortheHodgeLaplacian
10Isothermalcoordinatesandconformalstructuresonsurfaces
11Generalellipticboundaryproblems
12Operatorpropertiesofregularboundaryproblems
……
6LinearEvolutionEquations
AOutlineofFunctionaIAnalysis
BMarufoldsVectorBundlesandLieGroups
……