Enhanced Laplace transforms and desolve for Maxima
Subject: Enhanced Laplace transforms and desolve for Maxima
From: Richard Hennessy
Date: Tue, 25 Jan 2011 14:41:35 -0500
Hi Mark,
I was working on an inverse Fourier transform function for piecewise
functions for pw.mac (pwift()). I did not know of your work so I will
suspend my work on that. I really don't have the time to work on this stuff
anymore. I think your work is really great BTW.
It has been a long time since I have had any math courses. Is there a way
to do inverse Fourier transforms using ilt()? I can't remember.
Good luck,
Rich
-----Original Message-----
From: Mark H Weaver
Sent: Tuesday, January 25, 2011 11:51 AM
To: Hugo Coolens
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Enhanced Laplace transforms and desolve for Maxima
Hugo Coolens <coolens at kahosl.be> writes:
> Will the new code also deal with this:
> ilt(exp(-a*s)/s,s,t);
I didn't modify ilt to do this, but my new pwilt does it:
(%i2) load(pwilt)$
(%i3) pwilt(exp(-a*s)/s,s,t);
(%o3) hstep(t-a)
(%i4) pwilt(%e^-s*(s*%e^s-s^2-2*s-2)/s^3, s,t), ratsimp;
(%o4) t-t^2*hstep(t-1)
It is also designed to handle periodic functions
(though currently it fails to detect this in some cases):
(%i5) assume(a>0);
(%o5) [a > 0]
(%i6) pwilt(1/(s*(1-%e^-(2*a*s)))-%e^-(a*s)/(s*(1-%e^-(2*a*s))), s,t);
(%o6) 'sum(hstep(t-2*%k*a)-hstep(t-2*%k*a-a),%k,0,inf)
pwilt stands for "piecewise inverse laplace transform". I attached the
code at the beginning of this thread. In the other direction, my
changes to laplac.lisp support taking laplace transforms of piecewise
functions defined in terms of hstep or unit_step.
Note that this is still a work in progress.
Best,
Mark
> This would be great for (electronic) engineering students who want to
> make the shift to Maxima
>
>
> best regards,
> hugo
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