Mathematical Tools for Physics
Mathematical Tools for Physicsby James NearingPhysics DepartmentUniversity of 2003, James NearingPermission to copy forindividual or classroomuse is May, 2010ContentsIntroductioniiiBibliographyv 1Basic Stuff1TrigonometryParametric DifferentiationGaussian Integralserf and GammaDifferentiatingIntegralsPolar CoordinatesSketching Graphs2Infinite Series24The BasicsDeriving Taylor SeriesConvergenceSeries of SeriesPower series, two variablesStirling s ApproximationUseful TricksDiffractionChecking Results3Complex Algebra52Complex NumbersSome FunctionsApplications of Euler s FormulaGeometrySeries of cosinesLogarithmsMapping4Differential Equations67Linear Constant-CoefficientForced OscillationsSeries SolutionsSome General MethodsTrigonometry via ODE sGreen s FunctionsSeparation of VariablesCircuitsSimultaneous EquationsSimultaneous ODE sLegendre s EquationAsymptotic Behavior5Fourier Series100ExamplesComputing Fourier SeriesChoice of BasisMusical NotesPeriodically Forced ODE sReturn to ParsevalGibbs Phenomenon6Vector Spaces123The Underlying IdeaAxiomsExamples of Vector SpacesLinear IndependenceNormsScalar ProductBases and Scalar ProductsGram-Schmidt OrthogonalizationCauchy-Schwartz inequalityInfinite Dimensions7Operators and Matrices143The Idea of an OperatorDefinition of an OperatorExamples of OperatorsMatrix MultiplicationInversesRotations, 3-dAreas, Volumes.
Introduction. I wrote this text for a one semester course at the sophomore-junior level. Our experience with students taking our junior physics courses is that even if they’ve had the mathematical prerequisites,
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