偏微分方程(第1卷)(第2版)
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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
装帧平装
上书时间2024-12-03
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图书标准信息
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作者
[美]泰勒(Taylor M.E.) 著
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出版社
世界图书出版公司
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出版时间
2014-01
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版次
3
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ISBN
9787510068133
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定价
99.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
654页
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正文语种
英语
- 【内容简介】
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《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】
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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
……
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