complex-functions-examples-c-6 - calculus of residues.pdf

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1、Complex Functions Examples c6 Calculus of Residues Leif Mejlbro Download free books at LeifMejlbroComplexFunctionsExamplesc-6CalculusofResiduesComplexFunctionsExamplesc-6–CalculusofResidues©2008LeifMejlbro&VentusPublishingApSISBN978-87-7681-391-8ComplexFunktionsExamplesc-6ContentsCo

2、ntentsIntroduction51Rulesofcomputationofresidues62Residuesinnitesingularities93Lineintegralscomputedbymeansofresidues334Theresiduumat∞57Fast-trackyourcareerMastersinManagementStandoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusin

3、essSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthinkingandprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsultationwithrecruiterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull-timestudy,youwillgaintheb

4、usinessknowledgeandcapabilitiestoincreaseyourcareerchoicesandstandoutfromthecrowd.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sParkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.ed

5、uorcall+44(0)2070007573www.london.edu/mim/4ComplexFunktionsExamplesc-6IntroductionIntroductionThisisthesixthbookcontainingexamplesfromtheTheoryofComplexFunctions.Inthisvolumeweshallconsidertherulesofcalculationsorresidues,bothinfinitesingularitiesandin∞.ThetheoryheavilyreliesontheLau

6、rentseriesfromthefifthbookinthisseries.Theapplicationsofthecalculusofresiduesaregivenintheseventhbook.EvenifIhavetriedtobecarefulaboutthistext,itisimpossibletoavoiderrors,inparticularinthefirstedition.Itismyhopethatthereaderwillshowsomeunderstandingofmysituation.LeifMejlbro15thJune200

7、85ComplexFunktionsExamplesc-6Rulesofcomputationofresidues1RulesofcomputationofresiduesWereferingeneraltothefollowingrulesofcomputationofresidues:Definitionofaresiduum.Assumethatf(z)isananalyticfunctiondefinedinaneighbourhoodofz0∈C(notnecessarilyatz0itself)withtheLaurentseriesexpansio

8、n+∞f(z)=azn,0<

9、z

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