微分方程 MIT OpenCourseWare,Differential Equations,Spring,2004 英文版 DVD 只於電腦播放

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Thiscourseincludes講義,作業,problemsforgroupworkinrecitation,andafullsetoflecturevideos.
課程簡介CourseDescription

DifferentialEquationsarethelanguageinwhichthelawsofnatureareexpressed.Understandingpropertiesofsolutionsofdifferentialequationsisfundamentaltomuchofcontemporaryscienceandengineering.Ordinarydifferentialequations(ODE's)dealwithfunctionsofonevariable,whichcanoftenbethoughtofastime.Topicsinclude:Solutionoffirst-orderODE'sbyanalytical,graphicalandnumericalmethods;LinearODE's,especiallysecondorderwithconstantcoefficients;Undeterminedcoefficientsandvariationofparameters;Sinusoidalandexponentialsignals:oscillations,damping,resonance;Complexnumbersandexponentials;Fourierseries,periodicsolutions;Deltafunctions,convolution,andLaplacetransformmethods;Matrixandfirstorderlinearsystems:eigenvaluesandeigenvectors;andNon-linearautonomoussystems:criticalpointanalysisandphaseplanediagrams.