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).
>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/

```

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