Re: Laplace transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg29712] Re: [mg29687] Laplace transform*From*: "Mark Harder" <harderm at ucs.orst.edu>*Date*: Wed, 4 Jul 2001 03:08:36 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Knut, This is mostly a mathematical question about manipulating LaplaceTransforms of generalized functions; but it does demonstrate Mathematica's ability to handle the latter and to calculate the symbolic Laplace transforms for you. The trick is to replace G[t] with an expression in F[t] weighted by UnitStep[t-tm] , which =0 for t<tm, and 1 for t>=tm, namely G[t]:=F[t]*(1-UnitStep[t-tm]) +F[tm]*UnitStep[t-tm] . (See online documentation for definition of UnitStep) The enclosed notebook shows how this works for F[t]=Exp[-a t], symbolically, and graphically for a=tm=1. [Contact the author to obtain the notebook - moderator] -mark harder p.s. This problem has come up repeatedly, in which the solution is to replace a function defined in terms of an If[] condition on its arguments with some sort of generalized function construction. -----Original Message----- From: Knut Henning Schroder <Knut.Schroder at chembio.ntnu.no> To: mathgroup at smc.vnet.net Subject: [mg29712] [mg29687] Laplace transform >A function F(t) has the corresponding Laplace transform f(s), F(t) >increases with increasing t. >Another function G(t) is equal to F(t) up to a constant value of t = >tmax, and above that value G(t) = F(tmax) = Fmax. Fmax is a constant. >For some electrochemical calculations I need an expression for the >laplace transform of G(t). >Please assist me. >Regards, >Knut Schroder >Norwegian University of Science and Technology (NTNU), Department of Chemistry >N-7491 Trondheim, Norway. Tel: +47 73596205. Fax: +47 72556337 >EMAIL: Knut.Schroder at chembio.ntnu.no >http://www.kje.ntnu.no/~knusch/