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MathGroup Archive 2006

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Re: laplace transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65115] Re: laplace transform
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 15 Mar 2006 06:28:28 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <dv68hj$nvj$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

for real a the expression
Sqrt[a^2]*Sign[a] == Abs[a]*Sign[a]== a and you 
got

a/(a^2+s^2)

that corresponds to the answer of your mathematics 
book.
And for complex a you will see that
the Laplace transform doen not exist because for 
s=1/4 you get
NIntegrate[Sin[(0.3 + 0.5*I)*t]*Exp[-t/4], {t, 0, 
Infinity}]

an interseting result compared to your mathematics 
text book.

Regards
  Jens

<Marlies.Goorden at physics.unige.ch> schrieb im 
Newsbeitrag news:dv68hj$nvj$1 at smc.vnet.net...
| 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
| 



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