Robert KaramagiMay 26, 20191 min readDifferential EquationsUpdated: Jun 26, 2019 Basic ConceptsDefinitionsDirection FieldsThoughtsFirst Order Linear - iLinear - iiSeparable Equations - iSeparable Equations - iiExact - iExact - iiBernoulliSubstitutionsIntervals Of ValidityModeling - iModeling - iiEquilibrium SolutionsEuler's MethodSecond OrderBasic ConceptsReal & Distinct RootsComplex RootsRepeated RootsReduction of OrderFundamental Sets of SolutionsWronskian ApplicationsNon-homogeneousUndetermined Coefficients - iUndetermined Coefficients - iiUndetermined Coefficients - iiiVariation of Parameters – iVariation of Parameters – iiMechanical Vibrations – iMechanical Vibrations – iiLaplace TransformsDefinitionExamplesInverse – iInverse – iiStep Functions – iStep Functions – iiStep Functions – iiiSolving Initial Value Problems – iSolving Initial Value Problems – iiNonconstant Coefficient IVP'sIVP's With Step Functions – iIVP's With Step Functions – iiDirac Delta FunctionConvolution IntegralsTableSystemsEquationsMatrices & Vectors – iMatrices & Vectors – iiMatrices & Vectors – iiiEigenvalues & Eigenvectors – iEigenvalues & Eigenvectors – iiExamplesSolutionsPhase PlaneReal Eigenvalues – iReal Eigenvalues – iiComplex EigenvaluesRepeated Eigenvalues – iRepeated Eigenvalues – iiNon-homogeneousLaplace TransformsModelingSeries SolutionsPower Series – iPower Series – iiTaylorExamples – iExamples – iiExamples – iiiExamples – ivEuler EquationsHigher OrderBasic ConceptsLinear HomogeneousUndetermined CoefficientsVariation of Parameters – iVariation of Parameters – iiLaplace TransformsSeries SolutionsFourier SeriesBoundary Value Problems - iBoundary Value Problems - iiBoundary Value Problems - iiiEigenvalues and Eigenfunctions – iEigenvalues and Eigenfunctions – iiEigenvalues and Eigenfunctions - iiiPeriodic & Orthogonal Functions – iPeriodic & Orthogonal Functions - iiSine – iSine – iiSine - iiiCosine – iCosine – iiCosine – iiiExamples – iExamples – iiExamples - iiiConvergence
Basic ConceptsDefinitionsDirection FieldsThoughtsFirst Order Linear - iLinear - iiSeparable Equations - iSeparable Equations - iiExact - iExact - iiBernoulliSubstitutionsIntervals Of ValidityModeling - iModeling - iiEquilibrium SolutionsEuler's MethodSecond OrderBasic ConceptsReal & Distinct RootsComplex RootsRepeated RootsReduction of OrderFundamental Sets of SolutionsWronskian ApplicationsNon-homogeneousUndetermined Coefficients - iUndetermined Coefficients - iiUndetermined Coefficients - iiiVariation of Parameters – iVariation of Parameters – iiMechanical Vibrations – iMechanical Vibrations – iiLaplace TransformsDefinitionExamplesInverse – iInverse – iiStep Functions – iStep Functions – iiStep Functions – iiiSolving Initial Value Problems – iSolving Initial Value Problems – iiNonconstant Coefficient IVP'sIVP's With Step Functions – iIVP's With Step Functions – iiDirac Delta FunctionConvolution IntegralsTableSystemsEquationsMatrices & Vectors – iMatrices & Vectors – iiMatrices & Vectors – iiiEigenvalues & Eigenvectors – iEigenvalues & Eigenvectors – iiExamplesSolutionsPhase PlaneReal Eigenvalues – iReal Eigenvalues – iiComplex EigenvaluesRepeated Eigenvalues – iRepeated Eigenvalues – iiNon-homogeneousLaplace TransformsModelingSeries SolutionsPower Series – iPower Series – iiTaylorExamples – iExamples – iiExamples – iiiExamples – ivEuler EquationsHigher OrderBasic ConceptsLinear HomogeneousUndetermined CoefficientsVariation of Parameters – iVariation of Parameters – iiLaplace TransformsSeries SolutionsFourier SeriesBoundary Value Problems - iBoundary Value Problems - iiBoundary Value Problems - iiiEigenvalues and Eigenfunctions – iEigenvalues and Eigenfunctions – iiEigenvalues and Eigenfunctions - iiiPeriodic & Orthogonal Functions – iPeriodic & Orthogonal Functions - iiSine – iSine – iiSine - iiiCosine – iCosine – iiCosine – iiiExamples – iExamples – iiExamples - iiiConvergence