Transcription of Mathematical Tools for Physics
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Mathematical Tools for Physics
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 inequalityInfinite Dimensions7 Operators and Matrices143 The Idea of an OperatorDefinition of an
8 Multivariable Calculus 179 Partial Derivatives Chain Rule Di erentials Geometric Interpretation ... Vectors: Cylindrical, Spherical Bases i. Gradient in other Coordinates Maxima, Minima, Saddles Lagrange Multipliers Solid Angle Rainbow 9 Vector Calculus 1 213 Fluid Flow Vector Derivatives ... 16 Calculus of Variations 383 Examples Functional ...
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