目錄
Part1 DifferentialEquation微分方程式第1章 First-OrderDifferentialEquations一階常微分方程式1.1 GeneralandParticularSolution普解與特解1.2 TosolveFirst-OrderDifferentialEquations解一階常微分方程式1.2.1 SeparableDifferentialEquations分離式微分方程式1.2.2 HomogeneousDifferentialEquation齊次型微分方程式1.3 ExactDifferentialEquations正合式微分方程式1.3.1 ExactForm-usingIntegratingFactor正合式－利用積分因子1.3.2 TodeterminetheIntegratingFactor求取積分因子1.4 First-OrderLinearDifferentialEquations一階線性微分方程式1.5 Bernoulli'sEquation伯努利方程式1.6 ApplicationstoElectricalCircuit電路應用第2章 Second-OrderOrdinaryDifferentialEquations二階常微分方程式2.1 SecondOrderDifferentialEquation二階微分方程式2.2 ConstantCoefficientsofSecondOrderHomogeneousEquations二階常係數齊性方程式2.2.1 TwoDistinct,RealRoots二不等實根2.2.2 EqualRoots等根2.2.3 Complex,ConjugateRoots二共軛複數根2.3 WronskianTestForLinearIndependenceofSolutions朗斯基線性獨立之解2.4 ConstantCoefficientsofSecondOrderNon-HomogeneousEquations二階常係數非齊性方程式2.4.1 UndeterminedCoefficients未定係數法2.4.2 VariationofParameters參數變換法2.5 Euler-CauchyDifferentialEquations尤拉－柯西微分方程式2.5.1 Solutionoftheform之解2.5.2 SolutionbyOperatorDmethods微分運算子之解Part2 LaplaceTransform拉普拉斯轉換第3章 LaplaceTransformFundamental拉普拉斯轉換之基礎3.1 LaplaceTransform(L.T.)ofsomecommonFunctions拉普拉斯轉換的普通函數3.2 FirstShiftingProperty(S-Shifting)第一轉移定理(S-軸轉移)3.3 InverseLaplaceTransform拉普拉斯反轉換3.4 LaplaceTransformofDerivative拉普拉斯微分轉換3.5 LaplaceTransformofIntegral拉普拉斯積分轉換3.6 TheInitialandFinalvalueoff(t)fromF(s)初值與終值定理第4章 LaplaceTransformFunction拉普拉斯轉換之函數4.1 HeavisideUnitStepFunction單位階梯函數4.1.1 LaplaceTransformof拉普拉斯轉換4.1.2 LaplaceTransformof拉普拉斯轉換4.1.3 LaplaceTransformof拉普拉斯轉換4.1.4 TheSecondShiftinverseTheorem第二轉移反轉換定理4.2 PulseFunction脈波函數4.3 LaplaceTransformofImpulseFunction脈衝函數拉普拉斯轉換4.3.1 IntegrationInvolvingtheImpulseFunction脈衝函數積分轉換4.3.2 LaplaceTransformof拉普拉斯轉換4.3.3 LaplaceTransformof拉普拉斯轉換4.4 LaplaceTransformofPeriodicFunctions拉普拉斯週期函數4.5 ConvolutionTheorem摺積定理4.6 LaplaceTransformApplicationonElectricalCircuit拉普拉斯電路設計應用Part3 LinearAlgebra線性代數第5章 MatricesandDeterminants矩陣與行列式5.1 MatricesConcepts基本矩陣概念5.2 BasicpropertiesofMatrices矩陣的基本性質5.3 SpecialMatrices特別的矩陣5.4 Determinant行列式5.4.1 MinorandCofactors子式與餘因子5.4.2 Cofactorexpansionofadeterminantofanyorder行列式任何階之餘因子展開5.4.3 TheAdjointofasquarematrix方矩陣之伴隨5.4.4 TheInverseofamatrix反矩陣5.5 SystemsofLinearEquations線性方程系統5.5.1 SolutionofAx=b解Ax=b5.5.2 Solutionbymatrixinversion反矩陣之解5.5.3 SolutionbyCramer'sRule克蘭默法則5.5.4 SolutionbyElementaryRowOperation(ERO)基本列運算5.6 EigenvaluesandEigenvectors特微值與特微向量5.7 MatrixDiagonalization矩陣的對角線化Part4 FourierEquation傅立葉方程式第6章 FourierSeries傅立葉級數6.1 PeriodicFunctions週期函數6.1.1 EvenandOddfunctions偶函數和奇函數6.1.2 OddPlusConstantFunction奇數加常數之函數6.1.3 Half-wavesymmetry半波對稱6.2 FourierSeriesCoefficient傅立葉級數之係數6.3 FourierSeriesFunctions傅立葉級數之函數6.3.1 SineandCosineFunctionsofFourierSeries傅立葉級數之正弦與餘弦函數6.3.2 OddplusConstantPeriodicFunctionsofFourierSeries傅立葉級數之奇數加常數之週期函數6.3.3 Half-waveSymmetryFunctionsofFourierSeries傅立葉級數之半波對稱函數6.4 FourierSeriesMagnitudePhaseAngleForm傅立葉級數之振幅相位角型式6.5 FourierSeriesExponentialForm傅立葉級數之複數型式第7章 FourierAnalysis傅立葉分析7.1 FourierExpansion傅立葉展開7.2 FourierIntegral傅立葉積分7.2.1 ComplexFourierIntegral傅立葉複數積分7.2.2 FourierTrigonometricIntegral傅立葉三角積分7.2.3 FourierCosineandSineIntegral傅立葉餘弦與正弦積分7.3 FourierTransform傅立葉轉換
Part1 DifferentialEquation微分方程式第1章 First-OrderDifferentialEquations一階常微分方程式1.1 GeneralandParticularSolution普解與特解1.2 TosolveFirst-OrderDifferentialEquations解一階常微分方程式1.2.1 SeparableDifferentialEquations分離式微分方程式1.2.2 HomogeneousDifferentialEquation齊次型微分方程式1.3 ExactDifferentialEquations正合式微分方程式1.3.1 ExactForm-usingIntegratingFactor正合式－利用積分因子1.3.2 TodeterminetheIntegratingFactor求取積分因子1.4 First-OrderLinearDifferentialEquati...
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