(Rybkin)Mathematical Physics

《(Rybkin)Mathematical Physics》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、MATH611/612:MathematicalPhysicsLectureNotesAlexeiRybkinUniversityofAlaskaFairbanksContentsPart1.ComplexAnalysis9Lecture1.ComplexNumbers.FunctionsofComplexVariables111.ImaginaryUnit112.PropertiesofComplexNumbers113.ComplexFunctions13Lecture2.TheConceptofAnalyticFunction.TheCauch

2、y-RiemannConditions151.AnalyticFunctions152.Cauchy-RiemannConditions163.TheCauchyTheorem18Lecture3.TheCauchyIntegral231.IntroductoryExample232.CauchyIntegral23Appendix.TheMoreraTheorem26Lecture4.ComplexSeries291.NumericalSeries292.FunctionalSeries303.PowerSeries304.TaylorandLau

3、rentSeries31Lecture5.SingularitiesofAnalyticFunctionsandtheResidueTheorem371.Singularities372.Residues38Lecture6.ApplicationsoftheResidueTheoremtoEvaluationofSomeDeniteIntegrals4321.IntegralsofthetypeR(cos;sin)d43012.Integralsofthetypef(x)dx4411ix3.Integralsofthetypee

4、f(x)dx461Lecture7.ApplicationsoftheResidueTheoremtoSomeImproperIntegralsandIntegralsInvolvingMultivaluedFunctions491.IndentedContoursandCauchyPrincipalValues4934CONTENTS112.Integralsofthetypexf(x)dx;0<<1500Part2.LinearSpaces53Lecture8.VectorSpaces551.BasicDenitions552.Base

5、s563.Coordinates584.Subspaces58Lecture9.LinearOperators591.LinearOperator592.Matrices593.MatrixRepresentationofLinearOperators614.MatrixRing635.NoncommutativeRing64Lecture10.InnerProduct.SelfadjointandUnitaryOperators671.InnerProduct672.AdjointandSelfadjointOperators703.Unitary

6、Operators71Lecture11.MoreaboutSelfadjointandUnitaryOperators.ChangeofBasis731.ExamplesofSelfadjointandUnitaryOperators732.ChangeofBasis74Lecture12.EigenvaluesandEigenvectors771.Eigenvalues772.SpectralAnalysis78Part3.HilbertSpaces81Lecture13.Innitedimensionalspaces.HilbertSpace

7、s831.InniteDimensionalSpaces832.Basis833.NormedSpaces834.HilbertSpaces85Lecture14.L2{spaces.ConvergenceinNormedSpaces.BasisandCoordinatesinNormedandHilbertSpaces871.L2{spaces872.Convergenceinnormedspaces893.BasesandCoordinates90Lecture15.FourierSeries91Lecture16.SomeApplicatio

8、nsofFourierSeries95CONTENTS51.SignalProcessing952.Solv