complex-functions-examples-c-2 analytic functions.pdf

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1、Complex Functions Examples c2 Analytic Functions Leif Mejlbro Download free books at LeifMejlbroComplexFunctionsExamplesc-2AnalyticFunctionsComplexFunctionsExamplesc-2–AnalyticFunctions©2008LeifMejlbro&VentusPublishingApSISBN978-87-7681-384-0ComplexFunktionsExamplesc-

2、2ContentsContentsIntroduction51Somenecessarytheoreticalresults62Topologicalconcepts93ComplexFunctions124Limits405Lineintegrals466Dierentiableandanalyticfunctions;Cauchy-Riemann’sequations687ThepolarCauchy-Riemann’sequations978Cauchy’sIntegralTheorem1119Cauchy’sIntegra

3、lFormula11310SimpleapplicationsinHydrodynamics123Fast-trackyourcareerMastersinManagementStandoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthinking

4、andprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsultationwithrecruiterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull-timestudy,youwillgainthebusinessknowledgeandcapabilitiestoincreaseyourcareerchoice

5、sandstandoutfromthecrowd.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sParkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)2070007573www.london.edu/mim/

6、4ComplexFunktionsExamplesc-2IntroductionIntroductionThisisthesecondbookcontainingexamplesfromtheTheoryofComplexFunctions.Thefirsttopicwillbeexamplesofthenecessarygeneraltopologicalconcepts.Thenfollowsomeexamplesofcomplexfunctions,complexlimitsandcomplexlineintegrals.Fi

7、nally,wereachthesubjectitself,namelytheanalyticfunctionsingeneral.Themorespecificpropertiesoftheseanalyticfunctionswillbegiveninthebookstofollow.EvenifIhavetriedtobecarefulaboutthistext,itisimpossibletoavoiderrors,inparticularinthefirstedition.Itismyhopethatthereaderwil

8、lshowsomeunderstandingofmysituation.LeifMejlbro30thMay20085ComplexFunktionsExamplesc-2Somenecessarytheoreticalresults1Somene