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Re: laplace transform
 To: mathgroup at smc.vnet.net
 Subject: [mg65115] Re: laplace transform
 From: "JensPeer Kuska" <kuska at informatik.unileipzig.de>
 Date: Wed, 15 Mar 2006 06:28:28 0500 (EST)
 Organization: Uni Leipzig
 References: <dv68hj$nvj$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Hi,
for real a the expression
Sqrt[a^2]*Sign[a] == Abs[a]*Sign[a]== a and you
got
a/(a^2+s^2)
that corresponds to the answer of your mathematics
book.
And for complex a you will see that
the Laplace transform doen not exist because for
s=1/4 you get
NIntegrate[Sin[(0.3 + 0.5*I)*t]*Exp[t/4], {t, 0,
Infinity}]
an interseting result compared to your mathematics
text book.
Regards
Jens
<Marlies.Goorden at physics.unige.ch> schrieb im
Newsbeitrag news:dv68hj$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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