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Laplace Transform

  1. May 4, 2007 #1
    Hi all,

    Just a small question:
    I came across a problem to solve a differential equation using Laplace transform.

    I solved the major part but only still a part where I had to inverse transform the following experssion:


    I looked in Laplace Transform Tables but did not find it.

    Could you please help?
  2. jcsd
  3. May 7, 2007 #2


    User Avatar

    think i got it..

    you're looking for the integral..

    [tex] (2\pi i)^{-1} \oint ds exp(-st-s)/s^{2} [/tex]

    now using 'Residue theorem' you get...

    [tex] f(t)=0 [/tex] iff t<1 and f(t)=t/2 [/tex] iff t>1.

    depending on if you take the semi-circle (-T,0) or (0,T) with T--->oo , there is a double pole at s=0
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