傅立叶分析和偏微分方程

作者: R.Iorio 编 , M.Iorio V.de 编

出版社: 世界图书出版公司

出版时间: 2003-09

版次: 1

ISBN: 9787506265560

定价: 78.00

装帧: 平装

开本: 32开

纸张: 胶版纸

页数: 411页

分类: 自然科学

15人买过

ThisbookistheoutcomeofseveralcoursesandseminartalksheldattheInstitutodeMatematicaPuraeAplicada（IMPA）overtheyears.Itisagreatlymodifiedversionofapreviousworkbytheauthors,EquacoesDiferenciaisParciais,Umalntroducao,（ProjetoEuclides,IMPA,1978）.Ithasatwofoldpurpose,namelytointroducethestudenttothebasicconceptsofFourieranalysisandprovideillustrationsofrecentapplicationswheretheseconceptswereusedtostudyvariouspropertiesofthesolutionsofsomeimportantnonlinearevolutionequations. Preface
PartOne:FourierSeriesandPeriodicDistributions
1Preliminaries
1.1BasicDefinitionsandExamples
1.2ClassificationintoTypes
1.3Boundaryand/orInitialValueProblems
1.4SeparationofVariables:HeatFlowinaBar
1.5TheSchrodingerandtheWaveEquations
1.6TheDirichletProblemintheUnitCircle
1.7MaximumPrinciplesandUniqueness
2FourierSeries:BasicTheory
2.1SpacesofPeriodicFunctionsandSequences
2.2TheFourierTransform
2.3GeometricInterpretation
2.4DecayandDifferentiability
2.5TheInversionFormula:PointwiseConvergence
2.6PeriodicHeatFlow
2.7ApproximateIdentitiesandSummability
2.8CesaroSummability
3PeriodicDistributionsandSobolevSpaces
3.1CPeiodicFuncitons
3.2PerodicDistributions
3.3TopologicalRemakes
3.4FourierSeriesin
3.5TheConvolutionin
3.6SobolevSpaces

PartTwo:ApplicationstoPartialDfferentialEquations
4LinearEquations
5NonlinearEvolutionEquations
6TheKorteweg-deVriesEquation
7Distributions,FourierTransformandLinearEquations
8KdV,BOandFriends
AppendixAToolsfromtheTheoryofODEs
AppendixBCommutatorEstimates
Bibliography
Index
内容简介:
ThisbookistheoutcomeofseveralcoursesandseminartalksheldattheInstitutodeMatematicaPuraeAplicada（IMPA）overtheyears.Itisagreatlymodifiedversionofapreviousworkbytheauthors,EquacoesDiferenciaisParciais,Umalntroducao,（ProjetoEuclides,IMPA,1978）.Ithasatwofoldpurpose,namelytointroducethestudenttothebasicconceptsofFourieranalysisandprovideillustrationsofrecentapplicationswheretheseconceptswereusedtostudyvariouspropertiesofthesolutionsofsomeimportantnonlinearevolutionequations.
目录:
Preface
PartOne:FourierSeriesandPeriodicDistributions
1Preliminaries
1.1BasicDefinitionsandExamples
1.2ClassificationintoTypes
1.3Boundaryand/orInitialValueProblems
1.4SeparationofVariables:HeatFlowinaBar
1.5TheSchrodingerandtheWaveEquations
1.6TheDirichletProblemintheUnitCircle
1.7MaximumPrinciplesandUniqueness
2FourierSeries:BasicTheory
2.1SpacesofPeriodicFunctionsandSequences
2.2TheFourierTransform
2.3GeometricInterpretation
2.4DecayandDifferentiability
2.5TheInversionFormula:PointwiseConvergence
2.6PeriodicHeatFlow
2.7ApproximateIdentitiesandSummability
2.8CesaroSummability
3PeriodicDistributionsandSobolevSpaces
3.1CPeiodicFuncitons
3.2PerodicDistributions
3.3TopologicalRemakes
3.4FourierSeriesin
3.5TheConvolutionin
3.6SobolevSpaces

PartTwo:ApplicationstoPartialDfferentialEquations
4LinearEquations
5NonlinearEvolutionEquations
6TheKorteweg-deVriesEquation
7Distributions,FourierTransformandLinearEquations
8KdV,BOandFriends
AppendixAToolsfromtheTheoryofODEs
AppendixBCommutatorEstimates
Bibliography
Index

查看详情

傅立叶分析和偏微分方程

内容简介:

目录: