Designedforarigorousfirstcourseinordinarydifferentialequations,OrdinaryDifferentialEquations:IntroductionandQualitativeTheory,ThirdEditionincludesbasicmaterialsuchastheexistenceandpropertiesofsolutions,linearequations,autonomousequations,andstabilityaswellasmoreadvancedtopicsinperiodicsolutionsofnonlinearequations.Requiringonlyabackgroundinadvancedcalculusandlinearalgebra,thetextisappropriateforadvancedundergraduateandgraduatestudentsinmathematics,engineering,physics,chemistry,orbiology.ThisthirdeditionofahighlyacclaimedtextbookprovidesadetailedaccountoftheBendixsontheoryofsolutionsoftwo-dimensionalnonlinearautonomousequations,whichisaclassicalsubjectthathasbecomemoreprominentinrecentbiologicalapplications.ByusingthePoincarmethod,itgivesaunifiedtreatmentoftheperiodicsolutionsofperturbedequations.Thisincludestheexistenceandstabilityofperiodicsolutionsofperturbednonautonomousandautonomousequations(bifurcationtheory).Thetextshowshowtopologicaldegreecanbeappliedtoextendtheresults.ItalsoexplainsthatusingtheaveragingmethodtoseeksuchperiodicsolutionsisaspecialcaseoftheuseofthePoincarmethod.