vinogradov et al. canonical problems in scattering and potential theory. vol. 1 (crc, 2001)(364s)

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1、©2001CRCPressLLCToourchildren©2001CRCPressLLCContents1Laplace’sEquation1.1Laplace’sequationincurvilinearcoordinates1.1.1Cartesiancoordinates1.1.2Cylindricalpolarcoordinates1.1.3Sphericalpolarcoordinates1.1.4Prolatespheroidalcoordinates1.1.5Oblatespheroidalcoordinates1.1.6Ellipticcylindercoo

2、rdinates1.1.7Toroidalcoordinates1.2SolutionsofLaplace’sequation:separationofvariables1.2.1Cartesiancoordinates1.2.2Cylindricalpolarcoordinates1.2.3Sphericalpolarcoordinates1.2.4Prolatespheroidalcoordinates1.2.5Oblatespheroidalcoordinates1.2.6Ellipticcylindercoordinates1.2.7Toroidalcoordinat

3、es1.3Formulationofpotentialtheoryforstructureswithedges1.4Dualequations:aclassificationofsolutionmethods1.4.1Thedefinitionmethod1.4.2Thesubstitutionmethod1.4.3Noble’smultiplyingfactormethod1.4.4TheAbelintegraltransformmethod1.5Abel’sintegralequationandAbelintegraltransforms1.6Abel-typeintegra

4、lrepresentationsofhypergeometricfunctions1.7Dualequationsandsingle-ordouble-layersurfacepotentials2SeriesandIntegralEquations2.1DualseriesequationsinvolvingJacobipolynomials2.2Dualseriesequationsinvolvingtrigonometricalfunctions2.3DualseriesequationsinvolvingassociatedLegendrefunctions2.4Sy

5、mmetrictripleseriesequationsinvolvingJacobipolynomials2.4.1TypeAtripleseriesequations2.4.2TypeBtripleseriesequations©2001CRCPressLLC2.5Relationshipsbetweenseriesandintegralequations2.6DualintegralequationsinvolvingBesselfunctions2.7Nonsymmetricaltripleseriesequations2.8Coupledseriesequation

6、s2.9Aclassofintegro-seriesequations3ElectrostaticPotentialTheoryforOpenSphericalShells3.1Theopenconductingsphericalshell3.2Asymmetricalpairofopensphericalcapsandthesphericalbarrel3.2.1Approximateanalyticalformulaeforcapacitance3.3Anasymmetricalpairofsphericalcapsandtheasymmetricbarrel3.4The

7、methodofinversion3.5Electrostaticfieldsinasphericalelectroniclens3.6Frozenmagneticfieldsinsidesuperconductingshells3.7Screeningnumberofsuperconductingshells4ElectrostaticPotentialTheoryforOpenSpheroidalShells4.1Formulationofmixedboundaryvalueproblemsinsphe