Thefirsttwochaptersofthisbookhavebeenthoroughlyrevisedandsignificantlyexpanded.Sectionshavebeenaddedonelementarymethodsofintegration(onhomogeneousandinhomogeneousfirst-orderlinearequationsandonhomogeneousandquasi-homogeneousequations),onfirst-orderlinearandquasi-linearpartialdifferentialequations,onequationsnotsolvedforthederivative,andonSturmstheoremsonthezerosofsecond-orderlinearequations.Thustheneweditioncontainsallthequestionsofthecurrentsyllabusinthetheoryofordinarydifferentialequations.