... FiniteElementandFiniteDifferenceMethods 10 .6.1MathematicalFormulation 10 .6.2DiscussionoftheCode 10 .6.3NumericalResults 10 .7VibrationModesofanEllipticMembrane 10 .7.1AnalyticalFormulation 10 .7.2ComputerFormulation 11 BendingAnalysisofBeamsofGeneralCrossSection 11 .1Introduction 11 .1. 1AnalyticalFormulation 11 .1. 2ProgramtoAnalyzeBeamsofGeneralCrossSection 11 .1. 3ProgramOutputandCode 12 ApplicationsofAnalyticFunctions 12 .1PropertiesofAnalyticFunctions 12 .2DeÞnitionofAnalyticity 12 .3SeriesExpansions 12 .4IntegralProperties 12 .4.1CauchyIntegralFormula 12 .4.2ResidueTheorem 12 .5PhysicalProblemsLeadingtoAnalyticFunctions 12 .5.1Steady-StateHeatConduction 12 .5.2IncompressibleInviscidFluidFlow 12 .5.3TorsionandFlexureofElasticBeams 12 .5.4PlaneElastostatics 12 .5.5ElectricFieldIntensity 12 .6BranchPointsandMultivaluedBehavior 12 .7ConformalMappingandHarmonicFunctions 12 .8MappingontotheExteriorortheInteriorofanEllipse 12 .8.1ProgramOutputandCode 12 .9LinearFractionalTransformations 12 .9.1ProgramOutputandCode 12 .10 Schwarz-ChristoffelMappingontoaSquare 12 .10 .1ProgramOutputandCode 12 .11 DeterminingHarmonicFunctionsinaCircularDisk 12 .11 .1NumericalResults 12 .11 .2ProgramOutputandCode 12 .12 InviscidFluidFlowaroundanEllipticCylinder 12 .12 .1ProgramOutputandCode 12 .13 TorsionalStressesinaBeamMappedontoaUnitDisk 12 .13 .1ProgramOutputandCode 12 .14 StressAnalysisbytheKolosov-MuskhelishviliMethod 12 .14 .1ProgramOutputandCode© ... animation’), pause 11 6: % print -deps penangle 11 7: 11 8:nt=length(th); z=zeros(nt ,1) ; 11 9: x=[z,sin(th)]; y=[z,-cos(th)]; 12 0: hold off, close 12 1: if trac 12 2: axis([ -1, 1, -1, 1]), axis square, ... FiniteElementandFiniteDifferenceMethods 10 .6.1MathematicalFormulation 10 .6.2DiscussionoftheCode 10 .6.3NumericalResults 10 .7VibrationModesofanEllipticMembrane 10 .7.1AnalyticalFormulation 10 .7.2ComputerFormulation 11 BendingAnalysisofBeamsofGeneralCrossSection 11 .1Introduction 11 .1. 1AnalyticalFormulation 11 .1. 2ProgramtoAnalyzeBeamsofGeneralCrossSection 11 .1. 3ProgramOutputandCode 12 ApplicationsofAnalyticFunctions 12 .1PropertiesofAnalyticFunctions 12 .2DeÞnitionofAnalyticity 12 .3SeriesExpansions 12 .4IntegralProperties 12 .4.1CauchyIntegralFormula 12 .4.2ResidueTheorem 12 .5PhysicalProblemsLeadingtoAnalyticFunctions 12 .5.1Steady-StateHeatConduction 12 .5.2IncompressibleInviscidFluidFlow 12 .5.3TorsionandFlexureofElasticBeams 12 .5.4PlaneElastostatics 12 .5.5ElectricFieldIntensity 12 .6BranchPointsandMultivaluedBehavior 12 .7ConformalMappingandHarmonicFunctions 12 .8MappingontotheExteriorortheInteriorofanEllipse 12 .8.1ProgramOutputandCode 12 .9LinearFractionalTransformations 12 .9.1ProgramOutputandCode 12 .10 Schwarz-ChristoffelMappingontoaSquare 12 .10 .1ProgramOutputandCode 12 .11 DeterminingHarmonicFunctionsinaCircularDisk 12 .11 .1NumericalResults 12 .11 .2ProgramOutputandCode 12 .12 InviscidFluidFlowaroundanEllipticCylinder 12 .12 .1ProgramOutputandCode 12 .13 TorsionalStressesinaBeamMappedontoaUnitDisk 12 .13 .1ProgramOutputandCode 12 .14 StressAnalysisbytheKolosov-MuskhelishviliMethod 12 .14 .1ProgramOutputandCode©...