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Springer.Johnson.R.S.Singular.Perturbation.Theory.Mathematical.and.Analytical.Techniques.with.Applications.to.Engineering.(Springer.2005)

Springer.Johnson.R.S.Singular.Perturbation.Theory.Mathematical.and.Analytical.Techniques.with.Applications.to.Engineering.(Springer.2005)

ID：34894937

大小：6.44 MB

页数：309页

时间：2019-03-13

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1、SINGULARPERTURBATIONTHEORYMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGAlanJeffrey,ConsultingEditorPublished:InverseProblemsA.G.RammSingularPerturbationTheoryR.S.JohnsonForthcoming:MethodsforConstructingExac

2、tSolutionsofPartialDifferentialEquationswithApplicationsS.V.MeleshkoTheFastSolutionofBoundaryIntegralEquationsS.RjasanowandO.SteinbachStochasticDifferentialEquationswithApplicationsR.SituSINGULARPERTURBATIONTHEORYMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGR.S.JOHNSONSp

3、ringereBookISBN:0-387-23217-6PrintISBN:0-387-23200-1©2005SpringerScience+BusinessMedia,Inc.Print©2005SpringerScience+BusinessMedia,Inc.BostonAllrightsreservedNopartofthiseBookmaybereproducedortransmittedinanyformorbyanymeans,electronic,mechanical,recording,orotherwise,withoutwrittenconsent

4、fromthePublisherCreatedintheUnitedStatesofAmericaVisitSpringer'seBookstoreat:http://ebooks.springerlink.comandtheSpringerGlobalWebsiteOnlineat:http://www.springeronline.comToRos,whostill,afternearly40years,sometimeslistenswhenIextolthewondersofsingularperturbationtheory,fluidmechanicsorwat

5、erwaves—usuallyonalongtrekinthemountains.ThispageintentionallyleftblankCONTENTSForewordxiPrefacexiii1.Mathematicalpreliminaries11.1Someintroductoryexamples21.2Notation101.3Asymptoticsequencesandasymptoticexpansions131.4Convergentseriesversusdivergentseries161.5Asymptoticexpansionswithapara

6、meter201.6Uniformityorbreakdown221.7Intermediatevariablesandtheoverlapregion261.8Thematchingprinciple281.9Matchingwithlogarithmicterms321.10Compositeexpansions35FurtherReading40Exercises41viiiContents2.Introductoryapplications472.1Rootsofequations472.2Integrationoffunctionsrepresentedbyasy

7、mptoticexpansions552.3Ordinarydifferentialequations:regularproblems592.4Ordinarydifferentialequations:simplesingularproblems662.5Scalingofdifferentialequations752.6Equationswhichexhibitaboundary-layerbehaviour802.7Whereistheboundarylayer?862.8Boundarylayersand

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