singular perturbation theory - math and analyt technique w. appl to engineering - r. johnson

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1、SINGULARPERTURBATIONTHEORYMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGAlanJeffrey,ConsultingEditorPublished:InverseProblemsA.G.RammSingularPerturbationTheoryR.S.JohnsonFo

2、rthcoming:MethodsforConstructingExactSolutionsofPartialDifferentialEquationswithApplicationsS.V.MeleshkoTheFastSolutionofBoundaryIntegralEquationsS.RjasanowandO.SteinbachStochasticDifferentialEquationswithApplicationsR.SituSINGULARPERTURBATIONTHEORYMATHE

3、MATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGR.S.JOHNSONSpringereBookISBN:0-387-23217-6PrintISBN:0-387-23200-1©2005SpringerScience+BusinessMedia,Inc.Print©2005SpringerScience+BusinessMedia,Inc.BostonAllrightsreservedNopartofthiseBookmaybere

4、producedortransmittedinanyformorbyanymeans,electronic,mechanical,recording,orotherwise,withoutwrittenconsentfromthePublisherCreatedintheUnitedStatesofAmericaVisitSpringer'seBookstoreat:http://ebooks.springerlink.comandtheSpringerGlobalWebsiteOnlineat:htt

5、p://www.springeronline.comToRos,whostill,afternearly40years,sometimeslistenswhenIextolthewondersofsingularperturbationtheory,fluidmechanicsorwaterwaves—usuallyonalongtrekinthemountains.ThispageintentionallyleftblankCONTENTSForewordxiPrefacexiii1.Mathemat

6、icalpreliminaries11.1Someintroductoryexamples21.2Notation101.3Asymptoticsequencesandasymptoticexpansions131.4Convergentseriesversusdivergentseries161.5Asymptoticexpansionswithaparameter201.6Uniformityorbreakdown221.7Intermediatevariablesandtheoverlapregi

7、on261.8Thematchingprinciple281.9Matchingwithlogarithmicterms321.10Compositeexpansions35FurtherReading40Exercises41viiiContents2.Introductoryapplications472.1Rootsofequations472.2Integrationoffunctionsrepresentedbyasymptoticexpansions552.3Ordinarydifferen

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