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Does the dirac delta function have a Laplace transform?

  1. Jan 5, 2012 #1
    If yes, how can we find it?
     
  2. jcsd
  3. Jan 5, 2012 #2

    LCKurtz

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    The δ function isn't actually a function; it is a distribution. It can be thought of informally as the limiting case of a pulse$$
    f(t) = \left \{\begin{array}{rl}
    h, & 0 < t < \frac 1 h\\
    0,& \frac 1 h < t
    \end{array}\right.$$ Then, again informally, you can calculate its LaPlace transform by working$$
    \lim_{h\rightarrow \infty}\int_0^{\frac 1 h} he^{-st}\, dt$$ You should get an answer of 1.
     
    Last edited: Jan 5, 2012
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