化工应用数学

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1、化工應用數學授課教師：郭修伯Lecture6FunctionsanddefiniteintegralsVectorsChapter5FunctionsanddefiniteintegralsTherearemanyfunctionsarisinginengineeringwhichcannotbeintegratedanalyticallyintermsofelementaryfunctions.Thevaluesofmanyintegralshavebeentabulated,muchnumericalwork

2、canbeavoidediftheintegraltobeevaluatedcanbealteredtoaformthatistabulated.Ref.pp.153Wearegoingtostudysomeofthesespecialfunctions…..SpecialfunctionsFunctionsDetermineafunctionalrelationshipbetweentwoormorevariablesWehavestudiedmanyelementaryfunctionssuchaspolyn

3、omials,powers,logarithms,exponentials,trigonometricandhyperbolicfunctions.FourkindsofBesselfunctionsareusefulforexpressingthesolutionsofaparticularclassofdifferentialequations.Legendrepolynomialsaresolutionsofagroupofdifferentialequations.Learnsomemorenow….Th

4、eerrorfunctionItoccursinthetheoryofprobability,distributionofresidencetimes,conductionofheat,anddiffusionmatter:0xzerfxz:dummyvariableProofinnextslidexandyaretwoindependentCartesiancoordinatesinpolarcoordinatesErrorbetweenthevolumedeterminedbyx-yandr-Thevolu

5、meofhasabaseareawhichislessthan1/2R2andamaximumheightofe-R2MoreabouterrorfunctionDifferentiationoftheerrorfunction:Integrationoftheerrorfunction:Theaboveequationistabulatedunderthesymbol“ierfx”with(Therefore,ierf0=0)Anotherrelatedfunctionisthecomplementaryer

6、rorfunction“erfcx”Thegammafunctionforpositivevaluesofn.tisadummyvariablesincethevalueofthedefiniteintegralisindependentoft.(N.B.,ifniszerooranegativeinteger,thegammafunctionbecomesinfinite.)repeatThegammafunctionisthusageneralizedfactorial,forpositiveintegerv

7、aluesofn,thegammafunctioncanbereplacedbyafactorial.(Fig.5.3pp.147)MoreaboutthegammafunctionEvaluateChapter7VectoranalysisIthasbeenshownthatacomplexnumberconsistedofarealpartandanimaginarypart.Onesymbolwasusedtorepresentacombinationoftwoothersymbols.Itismuchqu

8、ickertomanipulateasinglesymbolthanthecorrespondingelementaryoperationsontheseparatevariables.Thisistheoriginalideaofvector.Anynumberofvariablescanbegroupedintoasinglesymbolintwoways:(1)Ma