Transcription of Mathematical Tools for Physics - Miami
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Mathematical Tools for Physics - Miami
Mathematical Tools for Physicsby James NearingPhysics DepartmentUniversity of 2003, James NearingPermission to copy forindividual or classroomuse is May, 2010 ContentsIntroductioniiiBibliographyv1 Basic Stuff1 TrigonometryParametric DifferentiationGaussian Integralserf and GammaDifferentiatingIntegralsPolar CoordinatesSketching Graphs2 Infinite Series24 The BasicsDeriving Taylor SeriesConvergenceSeries of SeriesPower series , two variablesStirling s ApproximationUseful TricksDiffractionChecking Results3 Complex Algebra52 Complex NumbersSome FunctionsApplications of Euler s FormulaGeometrySeries of cosinesLogarithmsMapping4 Differential Equations67 Linear Constant-CoefficientForced OscillationsSeries SolutionsSome General MethodsTrigonometry via ODE sGreen s FunctionsSeparation of VariablesCircuitsSimultaneous EquationsSimultaneous ODE sLegendre s EquationAsymptotic Behavior5 Fourier Series100 ExamplesComputing Fourier SeriesChoice of BasisMusical NotesPeriodically Forced ODE sReturn to ParsevalGibbs Phenomenon6 Vector Spaces123 The Underlying IdeaAxiomsExamples of Vector SpacesLinear IndependenceNormsScalar ProductBases and Scalar ProductsGram-Schmidt OrthogonalizationCauchy-Schwartz ineq
2 In nite Series 24 The Basics Deriving Taylor Series Convergence Series of Series Power series, two variables Stirling’s Approximation Useful Tricks Di raction ... Numerical Methods that (usually) Work by Acton. Mathematical Association of America Practical tools with more than the usual discussion of what can (and will) go wrong.
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