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1、ADVANCEDENGINEERINGMATHEMATICSwith®MATLABSECONDEDITIONADVANCEDENGINEERING®MATHEMATICSwithMATLABSECONDEDITIONDeanG.DuffyCHAPMAN&HALL/CRCACRCPressCompanyBocaRatonLondonNewYorkWashington,D.C.ThiseditionpublishedintheTaylor&Francise-Library,2009.Topurchaseyourownc
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3、eferencesarelisted.Reasonableeffortshavebeenmadetopublishreliabledataandinformation,buttheauthorandthepublishercannotassumeresponsibilityforthevalidityofallmaterialsorfortheconsequencesoftheiruse.Neitherthisbooknoranypartmaybereproducedortransmittedinanyformor
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6、edonlyforidentificationandexplanation,withoutintenttoinfringe.VisittheCRCPressWebsiteatwww.crcpress.com©2003byChapman&Hall/CRCNoclaimtooriginalU.S.GovernmentworksISBN0-203-00877-4Mastere-bookISBNInternationalStandardBookNumber1-58488-349-9ContentsDedicationAck
7、nowledgmentsIntroduction1ComplexVariables11.1ComplexNumbers11.2FindingRoots71.3TheDerivativeintheComplexPlane:TheCauchy-RiemannEquations11231.4LineIntegrals1.5TheCauchy-GoursatTheorem291.6Cauchy’sIntegralFormula331.7TaylorandLaurentExpansionsandSingularities37
8、1.8TheoryofResidues461.9EvaluationofRealDefiniteIntegrals521.10Cauchy’sPrincipalValueIntegral632First-OrderOrdinaryDifferentialEquations702.1ClassificationofDifferentialEquations70