palamodov v. topics in mathematical physics (tel aviv lectures, 2002)(80s)

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1、TopicsinMathematicalPhysicsProf.V.PalamodovSpringsemester2002ContentsChapter1:Di®erentialequationsofMathematicalPhysics1.1Di®erentialequationsofelliptictype1.2Di®usionequations1.3Waveequations1.4Systems1.5Nonlinearequations1.6Hamilton-Jacobitheory1.7Relati

2、vistic¯eldtheory1.8Classi¯cation1.9Initialandboundaryvalueproblems1.10InverseproblemsChapter2:Elementarymethods2.1Changeofvariables2.2Bilinearintegrals2.3Conservationlaws2.4Methodofplanewaves2.5Fouriertransform2.6TheoryofdistributionsChapter3:Fundamentalso

3、lutions3.1Basicde¯nitionandproperties3.2Fundamentalsolutionsforellipticoperators3.3Moreexamples3.4Hyperbolicpolynomialsandsourcefunctions3.5Wavepropagators3.6Inhomogeneoushyperbolicoperators3.7RieszgroupsChapter4:TheCauchyproblem4.1De¯nitions4.2Cauchyprobl

4、emfordistributions4.3HyperbolicCauchyproblem4.4SolutionoftheCauchyproblemforwaveequations4.5Domainofdependence2Chapter5:Helmholtzequationandscattering5.1Time-harmonicwaves5.2Sourcefunctions5.3Radiationconditions5.4Scatteringonobstacle5.5Interferenceanddi®r

5、actionChapter6:Geometryofwaves6.1Wavefronts6.2Hamilton-Jacobitheory6.3Geometryofrays6.4Anintegrablecase6.5Legendretransformationandgeometricduality6.6Ferm¶atprinciple6.7ThemajorHuygensprinciple6.8Geometricaloptics6.9Caustics6.10GeometricalconservationlawCh

6、apter7:ThemethodofFourierintegrals7.1Elementsofsymplecticgeometry7.2Generatingfunctions7.3Fourierintegrals7.4Lagrangedistributions7.5HyperbolicCauchyproblemrevisitedChapter8:Electromagneticwaves8.1Vectoranalysis8.2Maxwellequations8.3Harmonicanalysisofsolut

7、ions8.4Cauchyproblem8.5Localconservationlaws3Chapter1Di®erentialequationsofMathematicalPhysics1.1Di®erentialequationsofelliptictypeLetXbeanEuclideanspaceofdimensionnwithacoordinatesystemx1;:::;xn:²TheLaplaceequationis@2@2:¢u=0;¢=+:::+@x2@x21n¢iscalledtheLa

8、placeoperator.Asolutioninadomain•½Xiscalledharmonicfunctionin•.Itdescribesastablemembrane,electrostaticorgravity¯eld.²TheHelmholtzequation¡¢2¢+!u=0Forn=1itiscalledtheequationofharmonicoscillator.Asolutionisat