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MathGroup Archive 2006

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Re: laplace transform

  • To: mathgroup at
  • Subject: [mg65105] Re: laplace transform
  • From: "Scout" <Scout at>
  • Date: Wed, 15 Mar 2006 06:28:16 -0500 (EST)
  • References: <dv68hj$nvj$>
  • Sender: owner-wri-mathgroup at

<Marlies.Goorden at>
news:dv68hj$nvj$1 at
> Hi,
> I have a problem with the Laplace transform of mathematica. I
> want to know the laplace transform of sin(a*t).
> When I type
> LaplaceTransform[sin(a*t),t,s]
> mathematica gives me
> \sqrt(a^2) sign(a)/(a^2+s^2)
> On the other hand my mathematics books gives the answer
> a/(s^2+a^2)
> For complex a the answer is not the same. If I choose for
> example
> a=0.3+0.5i and
> s=1
> the two formulas give me
> -0.096+0.65i and 0.51+0.41i respectively.
> A numerical integration,
> i.e. NIntegrate[Sin((0.3+0.5i)*t)*Exp[-t],{t,0,Infinity}]
> gives me the same numerical value as the mathematics book
> formula.
> Is the mathematica formula wrong?
> Thank you for your help,
> Marlies Goorden
you might to use Assumptions with LaplaceTransform:


to obtain:  a/(s^2+a^2).


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