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1、Examples?of?Fourier?series?Leif?Mejlbro?Download?free?books?at?LeifMejlbroExamplesofFourierseriesCalculus4c-1ExamplesofFourierseries–Calculus4c-1?2008LeifMejlbro&VentusPublishingApSISBN978-87-7681-380-2ExamplesofFourierseriesContentsContentsIntroduction51.SumfunctionofFourierseries62.Fourierserie
2、sanduniformconvergence623.Parseval’sequation1014.Fourierseriesinthetheoryofbeams115Fast-trackyourcareerMastersinManagementStandoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthi
3、nkingandprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsultationwithrecruiterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull-timestudy,youwillgainthebusinessknowledgeandcapabilitiestoincreaseyourcareerchoicesandstandoutfromthecrowd
4、.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sParkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)2070007573www.london.edu/mim/4ExamplesofFourierseriesIntroductionIntroductionHerew
5、epresentacollectionofexamplesofapplicationsofthetheoryofFourierseries.ThereaderisalsoreferredtoCalculus4baswellastoCalculus3c-2.ItshouldnolongerbenecessaryrigourouslytousetheADIC-model,describedinCalculus1candCalculus2c,becausewenowassumethatthereadercandothishimself.EvenifIhavetriedtobecarefulab
6、outthistext,itisimpossibletoavoiderrors,inparticularinthe?rstedition.Itismyhopethatthereaderwillshowsomeunderstandingofmysituation.LeifMejlbro20thMay20085ExamplesofFourierseriesSumfunctionofFourierseries1SumfunctionofFourierseriesAgeneralremark.Insometextbookstheformulationofthemaintheoremalsoinc
7、ludestheunnecessaryassumptionthatthegraphofthefunctiondoesnothaveverticalhalftangents.Itshouldbereplacedbytheclaimthatf∈L2overthegivenintervalofperiod.However,sincemostpeopleonlyknowtheoldversion,Ihavecheckedinallexamp
