Laplace_Transforms.pdf

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1、TABLEOFLAPLACETRANSFORMSRevisionJByTomIrvineEmail:tomirvine@aol.comSeptember20,2011OperationTransformsNF(s)f(t),t>01.1Y(s)exp(st)y(t)dty(t),definitionofLaplacetransform01cjy(t)exp(st)Y(s)ds1.2Y(s)j2cjinversionformula1.3sYsy0y(t),firstderivative1.4s2Yssy(0)y(0)y(t),secondderi

2、vativesnYssn1[y(0)]1.5sn2[y(0)]s[y(n2)(0)]y(n)(t),nthderivative(n1)[y(0)]1t1.6FsY()d,integrations0t1.7F(s)G(s)f(t)g()d,convolutionintegral01s1.8Ff(t),scaling1.9F(s-)exp(t)f(t),shiftinginthesplane1sexptf(t),1.10Fcombinedscalingandshifting1FunctionTrans

3、formsNF(s)f(t),t>02.11t,unitimpulseatt=02.2sd(t),doubletimpulseatt=0dt2.3exp(-s(t)1u(t),unitstep2.4s12.5exp(s)u(t)s12.6t2s1n12.7,n1,2,3,....tns(n1)!n!2.8,n1,2,3,....nsn1t1k1,kisanyrealnumber>0tk,2.9s(k)theGammafunctionisgiveninAppendixA12.10exp(t)s1texp(t)2.112(s

4、)2FunctionTransformsNF(s)f(t),t>01tn12.12,n1,2,3,....exp(t)sn(n1)!2.131exp(t)ss112.14,exp(t)exp(t)ss11exp(t)exp(t)2.15,sss()()s12.16,exp(t)exp(t)sss2.1721texp(t)s112.18211texp(t)ss

5、22.19sint22ssin()scos()2.20sint22ss2.2122costs22s2.222tcost22s112.232221costss3FunctionTransformsNF(s)f(t),t>0112.24222sin(t)tcosts23s12.25222tsin(t)s22s1sin(t)tcost2.262222s1,1112.2722

6、22sintsintss2212.28t1expts2s2.29exptsints22s2.30exptcosts22s2.3122exptcostsintss222.32sint,arctan22s4FunctionTransformsNF(s)f(t),t>0112.33sinhts22s2.34cosh

7、t22s2.35arctan1ssintt112.36st112.37exptst1t2.382s35FunctionTransformsNF(s)f(t),t>013.1Jo(t),22sBesselfunctiongiveninAppendixA1t3.2223/2J1(t)s1Io(t),3.322Modif