complex-functions-examples-c-3 - elementary analytic function and harmonic functions.pdf

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1、Complex Functions Examples c3 Elementary Analytic Functions and Harmonic Functions Leif Mejlbro Download free books at LeifMejlbroComplexFunctionsExamplesc-3ElementaryAnalyticFunctionsandHarmonicFunctionsComplexFunctionsExamplesc-3–ElementaryAnalyticFunctionsandHarmonicF

2、unctions©2008LeifMejlbro&VentusPublishingApSISBN978-87-7681-387-1ComplexFunctionsExamplesc-3ContentsContentsIntroduction51.Somenecessarytheoreticalresults62.Polynomials123.Fractionalfunctions134.Theexponentialfunctionandthelogarithmfunction305.Trigonometricandhyperbolicf

3、unctions466.Harmonicfunctions62Fast-trackyourcareerMastersinManagementStandoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthinkingandprovideyouwiththef

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5、.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sParkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)2070007573www.london.edu/mim/4ComplexFunctionsExamplesc-

6、3IntroductionIntroductionThisisthethirdbookcontainingexamplesfromtheTheoryofComplexFunctions.Thefirsttopicwillbeexamplesofelementaryanalyticfunctions,likepolynomials,fractionalfunctions,exponentialfunctionsandthetrigonometricandthehyperbolicfunctions.Thenfollowsomeexample

7、sofharmonicfunctions.EvenifIhavetriedtobecarefulaboutthistext,itisimpossibletoavoiderrors,inparticularinthefirstedition.Itismyhopethatthereaderwillshowsomeunderstandingofmysituation.LeifMejlbro4thJune20085ComplexFunctionsExamplesc-3Somenecessarytheoreticalresults1Somenece

8、ssarytheoreticalresultsWestartwithTheorem1.1ThefundamentaltheoremofAlgebra.EverypolynomialP(z)ofdegreen