Re: laplace transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg65105] Re: laplace transform*From*: "Scout" <Scout at nodomain.com>*Date*: Wed, 15 Mar 2006 06:28:16 -0500 (EST)*References*: <dv68hj$nvj$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

<Marlies.Goorden at physics.unige.ch> 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 > Hi, you might to use Assumptions with LaplaceTransform: In[1]:= LaplaceTransform[Sin[a*t],t,s,Assumptions\[Rule]a\[Element]Reals] to obtain: a/(s^2+a^2). Bye, ~Scout~