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1、Complex?Functions?Examples?c5?Laurent?Series?Leif?Mejlbro?Download?free?books?at?LeifMejlbroComplexFunctionsExamplesc-5LaurentSeriesComplexFunctionsExamplesc-5–LaurentSeries?2008LeifMejlbro&VentusPublishingApSISBN978-87-7681-389-5ComplexFunktionsExamplesc-5Con
2、tentsContentsIntroduction51.Sometheoreticalbackground62.Laurentseries93.Fourierseries464.Laurentseriessolutionofdierentialequations495.Isolatedboundarypoints836.Theconditionsaroundthepointat∞96Fast-trackyourcareerMastersinManagementStandoutfromthecrowdDesigned
3、forgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthinkingandprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsultationwithrecru
4、iterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull-timestudy,youwillgainthebusinessknowledgeandcapabilitiestoincreaseyourcareerchoicesandstandoutfromthecrowd.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sP
5、arkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)2070007573www.london.edu/mim/4ComplexFunktionsExamplesc-5IntroductionIntroductionThisisthe?fthbookcontainingexamplesfromt
6、heTheoryofComplexFunctions.InthisvolumeweshallconsidertheLaurentseries,whichare,roughlyspeaking,complexpowerseriesinwhichwealsoallownegativeexponents.Weshallonlyconsiderthetheseriesandtheirrelationshiptothegeneraltheory,and?nallythetechniqueofsolvinglineardi?e
7、rentialequationswithpolynomialcoe?cientsbymeansofLaurentseries.TheimportanceoftheseLaurentserieswillbeshowninthefollowingbooks,wherewe?rstintroducetheresiduesinthesixthbook,andthenexamplesofapplicationsintheseventhbook.Thusthesethreebooks,thepresentoneandthetw
8、ofollowing,formtogethermakeupanimportantpartoftheTheoryofComplexFunctions.EvenifIhavetriedtobecarefulaboutthistext,itisimpossibletoavoiderrors,inparticularinthe?rstedition.Itismyho
