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 |