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1、ToAnna,mywifeSandroSalsaPartialDifferentialEquationsinActionFromModellingtoTheorySandroSalsaDipartimentodiMatematicaPolitecnicodiMilanoCIP-Code:2007938891ISBN978-88-470-0751-2SpringerMilanBerlinHeidelbergNewYorke-ISBN978-88-470-0752-9Thisworkissubjecttoco
2、pyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Duplicationofthispublicationorp
3、artsthereofispermittedonlyundertheprovisionsoftheItalianCopyrightLawinitscurrentversion,andpermissionforusemustalwaysbaobtainedfromSpringer.ViolationsareliabletoprosecutionundertheItalianCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.
4、comcSpringer-VerlagItalia,Milano2008PrintedinItalyCover-Design:SimonaColombo,MilanTypesettingwithLATEX:PTP-Berlin,Protago-TEX-ProductionGmbH,Germany(www.ptp-berlin.eu)PrintingandBinding:GrafichePorpora,Segrate(MI)987654321Springer-VerlagItaliasrl–ViaDece
5、mbrio28–20137Milano-IPrefaceThisbookisdesignedasanadvancedundergraduateorafirst-yeargraduatecourseforstudentsfromvariousdisciplineslikeappliedmathematics,physics,engineering.Ithasevolvedwhileteachingcoursesonpartialdifferentialequations(PDE)duringthelastfew
6、yearsatthePolitecnicoofMilan.Themainpurposeofthesecourseswastwofold:ontheonehand,totrainthestudentstoappreciatetheinterplaybetweentheoryandmodellinginprob-lemsarisingintheappliedsciences,andontheotherhandtogivethemasolidtheoreticalbackgroundfornumericalme
7、thods,suchasfiniteelements.Accordingly,thistextbookisdividedintotwoparts.Thefirstone,chapters2to5,hasaratherelementarycharacterwiththegoalofdevelopingandstudyingbasicproblemsfromthemacro-areasofdiffusion,prop-agationandtransport,wavesandvibrations.Ihavetried
8、toemphasize,wheneverpossible,ideasandconnectionswithconcreteaspects,inordertoprovideintuitionandfeelingforthesubject.Forthispart,aknowledgeofadvancedcalculusandordinarydifferentialequa-tionsisrequired.Also,therepeate
