mathematical tools for physics - j. nearing

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1、MathematicalToolsforPhysicsbyJamesNearingPhysicsDepartmentUniversityofMiamimailto:jnearing@miami.eduCopyright2003,JamesNearingPermissiontocopyforindividualorclassroomuseisgranted.QA37.2ContentsIntroduction.................iv4DifferentialEquations............83Lin

2、earConstant-CoefficientBibliography................viForcedOscillations1BasicStuff.................1SeriesSolutionsTrigonometryTrigonometryviaODE’sParametricDifferentiationGreen’sFunctionsGaussianIntegralsSeparationofVariableserfandGammaSimultaneousEquationsDifferent

3、iatingSimultaneousODE’sIntegralsLegendre’sEquationPolarCoordinates5FourierSeries...............118SketchingGraphsExamples2InfiniteSeries................30ComputingFourierSeriesTheBasicsChoiceofBasisDerivingTaylorSeriesPeriodicallyForcedODE’sConvergenceReturntoPar

4、sevalSeriesofSeriesGibbsPhenomenonPowerseries,twovariablesStirling’sApproximation6VectorSpaces...............142UsefulTricksTheUnderlyingIdeaDiffractionAxiomsCheckingResultsExamplesofVectorSpacesLinearIndependence3ComplexAlgebra..............65NormsComplexNumbers

5、ScalarProductSomeFunctionsBasesandScalarProductsApplicationsofEuler’sFormulaGram-SchmidtOrthogonalizationLogarithmsCauchy-SchwartzinequalityMappingInfiniteDimensionsi7OperatorsandMatrices..........168IntegralRepresentationofCurlTheIdeaofanOperatorTheGradientDefini

6、tionofanOperatorShorterCutfordivandcurlExamplesofOperatorsIdentitiesforVectorOperatorsMatrixMultiplicationApplicationstoGravityInversesGravitationalPotentialAreas,Volumes,DeterminantsSummationConventionMatricesasOperatorsMoreComplicatedPotentialsEigenvaluesandEi

7、genvectorsChangeofBasis10PartialDifferentialEquations.......283SummationConventionTheHeatEquationCanyouDiagonalizeaMatrix?SeparationofVariablesEigenvaluesandGoogleOscillatingTemperaturesSpatialTemperatureDistributions8MultivariableCalculus...........208SpecifiedHe

8、atFlowPartialDerivativesElectrostaticsDifferentialsChainRule11NumericalAnalysis............315GeometricInterpretationInterpolationGradientSolvingequationsElectrostatic