Laplace transform of periodic function
- To: mathgroup at smc.vnet.net
- Subject: [mg109180] Laplace transform of periodic function
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Fri, 16 Apr 2010 05:50:01 -0400 (EDT)
- Reply-to: murray at math.umass.edu
Is there some way to tell Mathematica that a function is periodic when
using LaplaceTransform to calculate its transform?
For example, if I define...
f[t_ /; 0 <= t < 1] :=
t - UnitStep[t - 1/2] t + UnitStep[t - 1/2] (1 - t)
f[t_] := f[t-1]
... and then try
LaplaceTransform[f[t], t, s]
... I get an $IterationLimit error.
Of course I can apply a standard formula to obtain the result:
f[t_] :=
t - UnitStep[t - 1/2] t + UnitStep[t - 1/2] (1 - t)
transformf[s_]=Integrate[Exp[-s t]f[t],{t,0,1}]/(1-Exp[-s])
But surely there's some way to force Mathematica to give the result of
the preceding through direct use of LaplaceTransform?
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305