complex-functions-examples-c-5 - laurent series.pdf

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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-5IntroductionIntroductionThisisthefifthbookcontainingexamplesfromt

6、heTheoryofComplexFunctions.InthisvolumeweshallconsidertheLaurentseries,whichare,roughlyspeaking,complexpowerseriesinwhichwealsoallownegativeexponents.Weshallonlyconsiderthetheseriesandtheirrelationshiptothegeneraltheory,andfinallythetechniqueofsolvinglineardiffe

7、rentialequationswithpolynomialcoefficientsbymeansofLaurentseries.TheimportanceoftheseLaurentserieswillbeshowninthefollowingbooks,wherewefirstintroducetheresiduesinthesixthbook,andthenexamplesofapplicationsintheseventhbook.Thusthesethreebooks,thepresentoneandthetw

8、ofollowing,formtogethermakeupanimportantpartoftheTheoryofComplexFunctions.EvenifIhavetriedtobecarefulaboutthistext,itisimpossibletoavoiderrors,inparticularinthefirstedition.Itismyho