Re: Problem with LaplaceTransform and InverseLaplaceTransform

*To*: mathgroup at smc.vnet.net*Subject*: [mg67510] Re: Problem with LaplaceTransform and InverseLaplaceTransform*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Thu, 29 Jun 2006 00:09:16 -0400 (EDT)*References*: <e7td5h$3kh$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

aXi wrote: >Can someone point me to site that would help me in using Mathematica >5.2for purpose of calculations related to Systhems theory. I'm having >trouble with several topics... for example doing >InverseLaplaceTransform of function: > >(1/s) * (TanH[pi*s/2]) > >Thanks in advance! > > > The form Exp[k*s]/s gives a step or cutoff function ( sometimes atributed to Heavyside). One method is to break it into a series and integrate the series: f[s_] = Normal[Series[(1/s) * (Tanh[Pi*s/2]), {s, 0, 30}]] g[t_] = InverseLaplaceTransform[f[s], s, t] The result is in DiracDelta function derivatives in even terms.