資源描述：
《VARIATIONAL METHODS FOR THE SOLUTION OF PROBLEMS OF EQUILIBRIUM AND VIBRATIONS_courant英文文獻(xiàn)資料》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、2165VARIATIONALMETHODSFORTHESOLUTIONOFPROBLEMSOFEQUILIBRIUMANDVIBRATIONSn.COURANTAsHenriPoincarConceremarked,“solutionofamathematicalproblem”isaphraseofindefinitemeaning.Puremathematicianssometimesaresatisfiedwithshowingthatthenon-existenceofasolutionimpliesalogicalcontra
2、diction,whileengineersmightcon-sideranumericalresultasthconlyreasonablegoal.Suchonesidedviewsseemtoreflecthumanlimitationsratherthanobjectivevalues.Initselfmathematicsisanindivisibleorganismunitingtheoreticalcontemplationandactiveapplication.Thisaddresswilldealwithatopici
3、nwhichsuchasynthesisoftheoreticalandappliedmathematicshasbecomeparticularlycon-vincing.SinceGaussandW.Thompson,theequivalencebetweenboundaryvalueproblemsofpartialdifferentialequationsontheonehandandproblemsofthecalculusofvariationsontheotherhandhasbeenacentralpointinanaly
4、sis.Atfirst,thetheoreticalin-terestinexistenceproofsdominatedandonlymuchlaterwereprac-ticalapplicationsenvisagedbytwophysicists,LordRayleighandWaltherRitz;theyindependentlyconceivedtheideaofutilizingthisequivalencefornumericalcalculationofthesolutions,bysubstitutingforthe
5、variationalproblemssimplerapproximatingextremumprob-lemsinwhichbutafinitenumberofparametersneedbedetermined.Rayleigh,inhisclassicalwork-Theoryofsound-andinotherpub-ications,wasthefirsttousesuchaprocedure.Butonlythespectacu-larsuccessofWaltherRitzanditstragiccircumstancesc
6、aughtthegeneralinterest.Intwopublicationsof1908and1909[39],Ritz,consciousofhisimminentdeathfromconsumption,gaveamasterlyaccountofthetheory,andatthesametimeappliedhismethodtothccalculationofthenodallinesofvibratingplates,aproblemofclassicalphysicsthatpreviouslyhadnotbeensa
7、tisfactorilytreated.Thusmethodsemergedwhichcouldnotfailtoattractengineersandphysicists;afteralr,theminimumprinciplesofmechanicsaremoresuggestivethanthedifferentialequations.Greatsuccessesinapplicationsweresoonfollowedbyfurtherprogressintheunder-standingofthetheoreticalbac
8、kground,andsuchprogressinturnmustresultinadvantagesfortheapplications.Anaddressdeliveredbeforeth
