elementary-analytic-functions.pdf

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1、Elementary Analytic Functions Complex Functions Theory a1 Leif Mejlbro Download free books at LeifMejlbroElementaryAnalyticFunctionsComplexFunctionsTheorya-12ElementaryAnalyticFunctions–ComplexFunctionsTheorya-1©2010LeifMejlbro&VentusPublishingApSISBN978-87-7681-690-23ElementaryAnalyti

2、cFunctionsContentsContentsIntroduction71TheComplexNumbers91.1Rectangularformofcomplexnumbers101.2Polarformofcomplexnumbers131.3Thebinomialequation201.4ThegeneralequationAz2+Bz+C=0ofseconddegree261.5Theequationsofthirdandfourthdegree27Theequationofthirddegree28Theequationoffourthdegree3

3、11.6Rationalrootsandmultiplerootsofapolynomial32Procedureofndingrationalroots33Procedureofndingmultipleroots351.7Symboliccurrentsandvoltages.Timevectors372BasicTopologyandComplexFunctions402.1BasicTopology40Topologyofopensets42Compactsets44Relativetopology48Fast-trackyourcareerMastersi

4、nManagementStandoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthinkingandprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsulta

5、tionwithrecruiterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull-timestudy,youwillgainthebusinessknowledgeandcapabilitiestoincreaseyourcareerchoicesandstandoutfromthecrowd.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sParkLondonNW14

6、SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)2070007573www.london.edu/mim/4ElementaryAnalyticFunctionsContentsConnectedsets50Uniformcontinuity55TheFixPointTheoremandsomeofitsconsequences562.2Complexfunctio

7、ns672.3Complexlimitsandcomplexsequences68Complexlimits69Complexsequences712.4Thecomplexinnityversustherealinnities722.5Complexlineintegrals74Complexcurves74Complexlineintegrals75Practicalcomputationofcomplexlineintegrals773AnalyticFunctions843.1Complexdifferentiablefunctionsandanalyt