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Laplace Sine Transform

  1. Oct 31, 2012 #1
    [itex]L[sin(at)]=\frac{a}{s^{2}+a^{2}}, Re>0[/itex]

    [itex]L[e^{kt}]=\frac{1}{s-k}, s>k[/itex]
    [itex]L[e^{-kt}]=\frac{1}{s+k}, s<-k[/itex]

    [itex]L[sin(at)]=\frac{1}{2i}L[e^{iat}-e^{-iat}][/itex]
    [itex]=\frac{1}{2i}L[e^{iat}]-L[e^{-iat}][/itex]
    Using the above relations
    [itex]=\frac{1}{2i}[\frac{1}{s-ia}-\frac{1}{s+ia}], s>ia, s<-ia[/itex]

    The problem is that I don't understand, how s>ia and s<-ia could imply that Real part of s>0?
     
  2. jcsd
  3. Nov 1, 2012 #2

    lurflurf

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    Homework Helper

    Complex numbers are not ordered,
    s>ia and s<-ia
    does not make sense.
    Real part of s>0
    Is needed to assure the existence of the integral.
     
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