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1、LAPLACETRANSFORMSMURRAYR.SPIEGEL,Ph.D.LaplacetransformsapplicationscompletelyvexplainedWorkswithallmajortexts450fullysolvedproblemsPerfectforbrushuporexamprepUsewiththesecourses:OperationalCalculus9ElectricalEngineering9MechanicsRTCollegeIkthematicsSCHAUM'SOUTLINEOFTHEORYANDPROBL
2、EMSOFLAPLACETRANSFORMS.MURRAYR.SPIEGEL,Ph.D.FormerProfessorandChairman.MathematicsDepartmentRensselaerPolytechnicInstituteHartfordGraduateCenter.SCHAUM'SOUTLINESERIESMcGRAW-HILLNewYorkSanFranciscoWashingtun.D.C.AucklandRogoidCaracasLisbonLondonMadridAlexienCity,MilanAluntrcalNewD
3、elhiSanJuanSingaporeSydneylbkva"lomnroCopyright©1965byMcGraw-Hill.Inc.AllRightsReserved.PrintedintheUnitedStatesofAmerica.Nopartofthispublicationmaybereproduced,storedinaretrieval-system,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,
4、withoutthepriorwrittenpermissionofthepublisher.6023112131415S11SH754321069PrefaceThetheoryofLaplacetransformsorLaplacetransformation,alsoreferredtoasoperationalcalculus,hasinrecentyearsbecomeanessentialpartofthemathematicalbackgroundrequiredofengineers,physicists,mathematiciansan
5、dotherscientists.Thisisbecause,inadditiontobeingofgreattheoreticalinterestinitself,Laplacetransformmethodsprovideeasyandeffectivemeansforthesolutionofmanyproblemsarisinginvariousfieldsofscienceandengineering.Thesubjectoriginatedinattemptstojustifyrigorouslycertain"operationalrule
6、s"usedbyHeavisideinthelatterpartofthe19thcenturyforsolvingequationsinelectro-magnetictheory.Theseattemptsfinallyprovedsuccessfulintheearlypartofthe20thcenturythroughtheeffortsofBromwich,Carson,vanderPolandothermathematicianswhoemployedcomplexvariabletheory.Thisbookisdesignedforus
7、easasupplementtoallcurrentstandardtextsorasatextbookforaformalcourseinLaplacetransformtheoryandapplications.Itshouldalsobeofconsiderablevaluetothosetakingcoursesinmathematics,physics,electricalengi-neering,mechanics,heatfloworanyofthenumerousotherfieldsinwhichLaplacetransformmeth
8、odsareemployed.Eachchapterbeginswithacle
