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