       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, 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)
>

```

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