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1、UniversitextRaviP.AgarwalDonalOReganAnIntroductiontoOrdinaryDifferentialEquationsRaviP.AgarwalDonalOReganFloridaInstituteofTechnologyNationalUniversityofIreland,GalwayDepartmentofMathematicalSciencesMathematicsDepartment150WestUniversityBlvd.UniversityRoadMelbourne,FL32901Galwa
2、y,Irelandagarwal@fit.edudonal.oregan@nuigalway.ieISBN:978-0-387-71275-8e-ISBN:978-0-387-71276-5DOI:10.1007/978-0-387-71276-5LibraryofCongressControlNumber:2007935982MathematicsSubjectClassification(2000):34-01,34-XX©2008SpringerScience+BusinessMediaLLCAllrightsreserved.Thisworkma
3、ynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMediaLLC,233SpringStreet,NewYork,NY10013,U.S.A.),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,
4、electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyar
5、esubjecttoproprietaryrights.Printedonacid-freepaper.987654321springer.comDedicatedtoRameshC.Guptaonhis65thbirthdayPrefaceOrdinarydifferentialequationsserveasmathematicalmodelsformanyexciting“real-world”problems,notonlyinscienceandtechnology,butalsoinsuchdiversefieldsaseconomics,p
6、sychology,defense,anddemography.Rapidgrowthinthetheoryofdifferentialequationsandinitsapplicationstoalmosteverybranchofknowledgehasresultedinacontinuedinterestinitsstudybystudentsinmanydisciplines.Thishasgivenordinarydifferen-tialequationsadistinctplaceinmathematicscurriculaallove
7、rtheworldanditisnowbeingtaughtatvariouslevelsinalmosteveryinstitutionofhigherlearning.Hundredsofbooksonordinarydifferentialequationsareavailable.How-ever,themajorityoftheseareelementarytextswhichprovideabatteryoftechniquesforfindingexplicitsolutions.Thesizeofsomeofthesebookshasgr
8、owndramatically—totheextentthatstudentsareoftenlostind
