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...Ordinary dierential equations peter philip lecture notes originally created for the class of spring semester at lmu munich revised and extended several subsequent classes september contents basic notions types first examples equivalent integral equation patching time reversion elementary solution methods geometric interpretation graphing linear ode variation constants separation variables change general theory equivalence between higher order systems existence solutions e mail math de uniqueness extension maximal continuity in initial conditions denition setting gronwall s inequality vector space fundamental matrix wronskian constant coecients stability qualitative phase portraits fixed points linearization limit sets a bernoulli is not an integer odd even b dierentiability c kn valued integration riemann lebesgue d local lipschitz on nonopen intervals f paths rn g functions product rule multiplication commute h autonomous nonautonomous with discontinuous right hand side i polar coordi...