工程數學－提升雙語&工程應用能力

目次1.1DifferentialEquation(DE)1.2FirstOrderDE1.3HomogeneousDE1.4NearHomogeneousDE1.5ExactDE1.6IntegratingFactorsandBernoulliDE1.7LinearDE1.8TheRiccatiDE1.9Applicationsofthe1stOrderDE1.10OrthogonalTrajectories1.11ExistenceandUniquenessofSolutionsofInitialValue1.12DirectionField1.13Picard'sIterationMethod1.14一般習題1.15電學系群相關應用題2.1LinearSecondOrderDE2.2ReductionofOrder2.3y"+Ay'+By=02.4TheCauchy-EulerDE2.5二階齊次DE的應用2.6NonhomogeneousSecondOrderDE2.7TheMethodofUndeterminedCoefficients2.8VariationofParameters2.9ForcedOscillations,Resonance,Beats,andElectricalC2.10一般習題2.11電學系群相關應用題3.1DE,Order3.2ConstantCoefficient,HomogeneousDE3.3n-thOrderCauchy-EulerDE3.4TheMethodsofUnderminedCoefficients(UC)andVariat3.5OperatorTechniques3.6一般習題3.7電學系群相關應用題4.1DefinitionandTheoryoftheLT4.2SolvingInitialValueProblemsUsingtheLT4.3TheFirstShiftingTheorem4.4TheHeavisideFunctionandtheSecondShifting4.5UnitImpulseandtheDiracDeltaFunction4.6SolutionofSystemsbytheLT4.7一般習題4.8電學系群相關應用題5.1SeriesSolutionsofDE5.2SingularPointsandtheMethodofFrobenius5.3SeriesExpansionsandOrthogonalSetsofFunctions5.4Sturm-LiouvilleTheoremandBoundaryValueProblems5.5一般習題5.6電學系群相關應用題6.1TheFirstProblemintheCOV6.2AnEulerEquationfor6.3IsoperimetricProblems6.4PrincipalComponentAnalysis6.5一般習題6.6電學系群相關應用題7.1VectorFunctionsofOneVariable7.2Velocity,Acceleration,Curvature,Torsion(扭率)7.3VectorFieldandLinesofForce7.4TheGradientVectorField7.5Divergence(散度)andCurl(旋度)7.6一般習題7.7電學系群相關應用題8.1LineIntegrals8.2Green'sTheorem8.3IndependenceofPathandPotentialTheoryinthePlane8.4SurfacesandSurfaceIntegral8.5TheDivergenceTheoremofGauss8.6ApplicationsoftheDivergenceTheorem8.7Stokes'sTheorem8.8一般習題8.9電學系群相關應用題9.1FourierSeries9.2Convergence,Differentiation,andIntegrationofFourie9.3FourierSine&CosineSeries9.4MultipleFourierSeries9.5PeriodicFunctionsandtheAmplitudeSpectrum9.6ComplexFourierSeries(CFS)andFrequencySpectra9.7FourierIntegral(FI)9.8TheFourierTransform(FT)9.9AdditionalPropertiesofF.T9.10FourierSineandCosineTransforms9.11一般習題9.12電學系群相關應用題10.1Introduction10.2FourierSeriesSolutionoftheWaveEquation10.3FourierSeriesSolutionoftheHeatEquation10.4Steady-StateTemperaturesinaFlatPlate10.5SolutionoftheHeatandWaveEquationsinUnboundedDo10.6SomeProblemsinwhichSeparationofVariablesFails10.7一般習題10.8電學系群相關應用題參考文獻縮寫中英文名詞對照與索引

目次1.1DifferentialEquation(DE)1.2FirstOrderDE1.3HomogeneousDE1.4NearHomogeneousDE1.5ExactDE1.6IntegratingFactorsandBernoulliDE1.7LinearDE1.8TheRiccatiDE1.9Applicationsofthe1stOrderDE1.10OrthogonalTrajectories1.11ExistenceandUniquenessofSolutionsofInitialValue1.12DirectionField1.13Picard'sIterationMethod1.14一般習題1.15電學系群相關應用題2.1LinearSecondOrderDE2.2ReductionofOrder2.3y"+Ay'+By=02.4TheCauchy-EulerDE2.5二階齊次DE的應用2.6NonhomogeneousSecondOrderDE2.7TheMethodofUndeterminedCoefficient...