偏微分方程（第1卷）

图书标准信息

• 作者 索维尼（Friedrich Sauvigny） 著
• 出版社 世界图书出版公司
• 出版时间 2011-06
• 版次 1
• ISBN 9787510035173
• 定价 55.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 437页
• 正文语种 英语

【内容简介】

Partialdifferentialequationsequallyappearinphysicsandgeometry.Withinmathematicstheyunitetheareasofcomplexanalysis,differentialgeome-tryandcalculusofvariations.Theinvestigationofpartialdifferentialequa-tionshassubstantiallycontributedtothedevelopmentoffunctionalanalysis.Thougharelativelyuniformtreatmentofordinarydifferentialequationsispossible,quitemultipleanddiversemethodsareavailableforpartialdifferen-tialequations.Withthistwo-volumetextbookweintendtopresenttheentiredomainPARTIALDIFFERENTIALEQUATIONS-sorichintheoriesandapplica-tions-tostudentsattheintermediatelevel.

【目录】

1DifferentiationandIntegrationonManifolds
TheWeierstrai
Parameter-invariantintegralsanddifferentialforms
Theexteriorderivativeofdifferentialforms
TheStokesintegraltheoremformanifolds
TheintegraltheoremsofGauandStokes
Curvilinearintegrals
ThelemmaofPoincare
Co-derivativesandtheLaplace-Beltramioperator
SomehistoricalnoticestochapterI

2FoundationsofFunctionalAnalysis
Daniell'sintegralwithexamples
ExtensionofDaniell'sintegraltoLebesgue'sintegral
Measurablesets
Measurablefunctions
Riemann'sandLebesgue'sintegralonrectangles
BanachandHilbertspaces
TheLebesguespacesLP（X）
BoundedlinearfunctionalsonLP（X）andweakconvergence.
SomehistoricalnoticestochapterII

3Brouwer'sDegreeofMappingwithGeometricApplications
Thewindingnumber
ThedegreeofmappinginRn
Geometricexistencetheorems
Theindexofamapping
Theproducttheorem

TheoremsofJordan-Brouwer
4GeneralizedAnalyticFunctions
TheCauchy-Riemanndifferentialequation
HolomorphicfunctionsinCn
GeometricbehaviorofholomorphicfunctionsinC
Isolatedsingularitiesandthegeneralresiduetheorem
TheinhomogeneousCauchy-Riemanndifferentialequation
Pseudoholomorphicfunctions
Conformalmappings
Boundarybehaviorofconformalmappings
SomehistoricalnoticestochapterIV

5PotentialTheoryandSphericalHarmonics
Poisson'sdifferentialequationinRn
Poisson'sintegralformulawithapplications
Dirichlet'sproblemfortheLaplaceequationinRn
Theoryofsphericalharmonics:Fourierseries
Theoryofsphericalharmonicsinnvariables

6LinearPartialDifferentialEquationsinRn
Themaximumprincipleforellipticdifferentialequations
Quasilinearellipticdifferentialequations
Theheatequation
Characteristicsurfaces
ThewaveequationinRnforn=1,3,2
ThewaveequationinRnforn_>2
Theinhomogeneouswaveequationandaninitial-boundary-
valueproblem
Classification,transformationandreductionofpartial
differentialequations
SomehistoricalnoticestothechaptersVandVI
References
Index