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