outlines_chp3_sections_f10

outlines_chp3_sections_f10 - 3.2Outline I.

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Unformatted text preview: 3.2Outline I. GeneralSystemofTwoFirstOrderLinearODE A.Matrixsetup B.Homogeneous/nonhomogeneous C.Autonomous/nonautonomous,equilibriumsolutions D.Existenceanduniqueness II. Terminology A.Statevariables,vector,plane B.Trajectory,orbit C.Directionfield,phaseportrait,componentplots III.TransformationofSecondOrderLinearODEtoSystemof FirstOrderLinearODE IV. Applications A.Tanks(exampleinbook) B.Circuits 3.3Outline I. HomogeneousLinearSystemwithConstant Coefficients II. Solutions A.Superposition B.Wronskian C.Fundamentalsetofsolutions D.Solutionformwitheigenvalues,realand unequal III. GraphicalIdeasandSolutions A.Originasnodalsink,nodalsource,saddle point B.Trajectorypatterns 3.4Outline I. ComplexSolutions II. SolutionstoODEwithComplexEigenvalues A.Complexformofsolution B.Realformofsolution III. GraphicalIdeasandSolutions A.Originasspiralsink,spiralsource,center 3.5Outline I. RepeatedEigenvalues II. Solutions A.Nondefective case B.Defectivecase(generalizedeigenvectors) III. GraphicalIdeasandSolutions A.Originaspropernode(star),improper node(degenerate) IV.SummaryofOriginAsTypesofNodes ...
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This note was uploaded on 02/07/2011 for the course MATH 333 taught by Professor Staff during the Spring '08 term at Boise State.

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