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1、Examples of Eigenvalue Problems Leif Mejlbro Download free books at LeifMejlbroExamplesofEigenvalueProblemsCalculus4c-2ExamplesofEigenvalueProblems–Calculus4c-2©2008LeifMejlbro&VentusPublishingApSISBN978-87-7681-381-9ExamplesofEigenvalueProblemsContentsContentsIntroductio
2、n51Initialandboundaryvalueproblems62Eigenvalueproblems143Nontypicaleigenvalueproblems67Fast-trackyourcareerMastersinManagementStandoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpa
3、ndyourPleaseclicktheadvertthinkingandprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsultationwithrecruiterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull-timestudy,youwillgainthebusinessknowledgeandcapabili
4、tiestoincreaseyourcareerchoicesandstandoutfromthecrowd.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sParkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)207
5、0007573www.london.edu/mim/4ExamplesofEigenvalueProblemsIntroductionIntroductionHerewepresentacollectionofexamplesofeigenvalueproblems.ThereaderisalsoreferredtoCalculus4baswellastoCalculus3c-2.ItshouldnolongerbenecessaryrigourouslytousetheADIC-model,describedinCalculus1can
6、dCalculus2c,becausewenowassumethatthereadercandothishimself.EvenifIhavetriedtobecarefulaboutthistext,itisimpossibletoavoiderrors,inparticularinthefirstedition.Itismyhopethatthereaderwillshowsomeunderstandingofmysituation.LeifMejlbro20thMay20085ExamplesofEigenvalueProblemsI
7、nitialandboundaryvalueproblems1InitialandboundaryvalueproblemsExample1.1Solvethefollowingeigenvalueproblemy+λy=0,x∈[0,L],y(0)=y(0)=0.Thisisapureinitialvalueproblemy(0)=0andy(0)=0,hencethesolutionisunique.Obviously,thezerosolutionistheonlysolutions.Example1.2Provethatt
8、heboundaryvalueproblemd2ydy+2+2y=0,x∈[0,π],y(0)=1,y(π)=−e−π,dx2dxhasinfinitelymanysolutionsandfind
