Re: Laplace Transforms of piecewise continuous functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg28301] Re: [mg28292] Laplace Transforms of piecewise continuous functions*From*: BobHanlon at aol.com*Date*: Mon, 9 Apr 2001 02:58:02 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

f[t_] := 3 - 5*UnitStep[t-2] + 2*UnitStep[t-3]; Plot[f[t], {t, 0, 4}, PlotStyle -> {AbsoluteThickness[2], RGBColor[1, 0, 0]}]; F[s_] := Evaluate[LaplaceTransform[f[t], t, s]]; F[s] 2/(E^(3*s)*s) - 5/(E^(2*s)*s) + 3/s InverseLaplaceTransform[F[s], s, t] -> f[t] True Bob Hanlon In a message dated 2001/4/7 4:01:11 AM, mapowers at email.com writes: >The documentation isn't very clear on how to compute a Laplace Transform >of >a piecewise continuous function f(t). Say I have a function f(t) such >that: > >f(t) = {3 over 0<=t<2, -2 over 2<=t<3, 0 over 3 <=t} > >how can I use the LaplaceTransform[] function to compute this easily? >(aside from separately integrating the pieces, and adding) >