an introduction to ordinary differential equations (agarwal o regan)

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1、UniversitextRaviP.AgarwalDonalOReganAnIntroductiontoOrdinaryDifferentialEquationsRaviP.AgarwalDonalOReganFloridaInstituteofTechnologyNationalUniversityofIreland,GalwayDepartmentofMathematicalSciencesMathematicsDepartment150WestUniversityBlvd.UniversityRoadMelbourne,FL32901Galway,Irela

2、ndagarwal@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.Thisworkmaynotbetranslat

3、edorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMediaLLC,233SpringStreet,NewYork,NY10013,U.S.A.),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,

4、computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.

5、Printedonacid-freepaper.987654321springer.comDedicatedtoRameshC.Guptaonhis65thbirthdayPrefaceOrdinarydifferentialequationsserveasmathematicalmodelsformanyexciting“real-world”problems,notonlyinscienceandtechnology,butalsoinsuchdiversefieldsaseconomics,psychology,defense,anddemography.Rap

6、idgrowthinthetheoryofdifferentialequationsandinitsapplicationstoalmosteverybranchofknowledgehasresultedinacontinuedinterestinitsstudybystudentsinmanydisciplines.Thishasgivenordinarydifferen-tialequationsadistinctplaceinmathematicscurriculaallovertheworldanditisnowbeingtaughtatvariouslev

7、elsinalmosteveryinstitutionofhigherlearning.Hundredsofbooksonordinarydifferentialequationsareavailable.How-ever,themajorityoftheseareelementarytextswhichprovideabatteryoftechniquesforfindingexplicitsolutions.Thesizeofsomeofthesebookshasgrowndramatically—totheextentthatstudentsareoftenlo

8、stind