GeorgeSimmonssfinetextisatraditionalbookwrittenintheclassicalstyle.Itprovidesacogentandaccessibleintroductiontoallthetraditionaltopics.Itisapleasuretohavethisopportunitytobringthistextuptodateandtoaddsomemoretimelymaterial.Wehavestreamlinedsomeoftheexpositionandaugmentedotherparts.ThereisnowcomputerworkbasednotonlyonnumbercrunchingbutalsooncomputeralgebrasystemssuchasMaple,Mathematica,andMATLAB.Certainlyastudyofflowsandvectorfields,andofthebeautifulPoincare-Bendixsontheorybuilttheorem,isessentialforanymoderntreatment.Onecanintroducesomeofthemodernideasfromthetheoryofdynamicstoobtainqualitativeinformationaboutnonlineardifferentialequationsandsystems.
Andalloftheaboveisabasisformodeling.Modelingiswhatbringsthesubjecttolifeandmakestheideasrealforthestudents:Differentialequationscanmodelreal-lifequestions,andcomputercalculationsandgraphicscanthenprovidereal-lifeanswers.Thesymbiosisofthesyntheticandthecalculationalprovidesaricheducationalexperienceforstudents,anditpreparesthemformoreconcrete,appliedworkinfuturecourses.ThenewAnatomyofanApplicationsectionsinthiseditionshowcasesomerichapplicationsfromengineering,physics,andappliedscience.