laplace transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg65076] laplace transform*From*: Marlies.Goorden at physics.unige.ch*Date*: Tue, 14 Mar 2006 05:59:53 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: laplace transform***From:*Pratik Desai <pdesai1@umbc.edu>