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Re: Help: piecewise functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50149] Re: Help: piecewise functions
  • From: "rik" <rikypi_ALLA_LARGA at libero.it>
  • Date: Wed, 18 Aug 2004 01:19:56 -0400 (EDT)
  • References: <cfi96d$4s5$1@smc.vnet.net> <cfshm9$9pq$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

thanks,
i know that D[UnitStep{t],t] "=" DiracDelta[t], in fact i need to separate
the really funciton's part from the definition of the intervall where this
funciton is defined (intervall in R, but i have a R^n space and my set are,
in general, polytopes).

The definition set of my function are like this:

S1 :=
(UnitStep[t1-3]-UnitStep[t1-5])(UnitStep[t2-t1]-UnitStep[t2-6])(UnitStep[t4-
t3]-UnitStep[t4-t2])

so i have something like this


/  f1 is (t1,...,tm) in S1

|  f2 is (t1,...,tm) in S2

|         .
g(t1,...,tm) := f1 S1 + f2 S2 + . . . + fj Sj + . . .+ fn Sn = |         .

|         .

\  fn is (t1,...,tm) in Sn


where  fj = fj(t1,...,tm) is a polinomial function in t1,...,tm defined over
Sj (Sj hs a structure  analogous to S1)


I need to integrate and do differentiation of g(t1,...,tm) and, obviously,
when i try to do this, Mathematica do the intergal or differentation not
only of f1,...,fn but also of UnitStep that are in Sj.

If you have same idea to do this...

P.S. i have  A LOT of this function, and i would a program that do the
operations :-)

by rik


"Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> ha scritto nel messaggio
news:cfshm9$9pq$1 at smc.vnet.net...
> Hi,
>
> perhaps D[UnitStep{t],t] is DiracDelta[t] and this is not a
> function, it is a distribution and distributions ar only allowed
> in integrals ...
>
> Regards
>   Jens
>
> rik wrote:
> >
> > hi,
> > i'm a italian student and i must integrate and do differentiation of
> > piecewise functions like this:
> >
> >  f[t1,t2,t3] ((UnitStep[t3-t1]-UnitStep[t3-4])
> > (UnitStep[t2-t1]-UnitStep[t2-5])) + g[t1,t2,t3]
> > ((UnitStep[t2]-UnitStep[t2-t1]) (UnitStep[t1-6]-UnitStep[t1-20])) + ...
> >
> > i would have  this:
> >
> > D[f[t1,t2,t3] ((UnitStep[t3-t1]-UnitStep[t3-4])
> > (UnitStep[t2-t1]-UnitStep[t2-5])) +
> >  g[t1,t2,t3] ((UnitStep[t2]-UnitStep[t2-t1])
> > (UnitStep[t1-6]-UnitStep[t1-20])) + ...] "="
> >  f'[t1,t2,t3] ((UnitStep[t3-t1]-UnitStep[t3-4])
> > (UnitStep[t2-t1]-UnitStep[t2-5]))  +
> > + g'[t1,t2,t3] ((UnitStep[t2]-UnitStep[t2-t1])
> > (UnitStep[t1-6]-UnitStep[t1-20])) +
> > + D[...]
> >
> > and this:
> >
> > Integrate[ f[t1,t2,t3] ((UnitStep[t3-t1]-UnitStep[t3-4])
> > (UnitStep[t2-t1]-UnitStep[t2-5])) +
> > g[t1,t2,t3] ((UnitStep[t2]-UnitStep[t2-t1])
> > (UnitStep[t1-6]-UnitStep[t1-20])) + ...] "="
> > Integrate[f[t1,t2,t3]] ((UnitStep[t3-t1]-UnitStep[t3-4])
> > (UnitStep[t2-t1]-UnitStep[t2-5])) +
> > + Integrate[g[t1,t2,t3]] ((UnitStep[t2]-UnitStep[t2-t1])
> > (UnitStep[t1-6]-UnitStep[t1-20])) +
> > + Integrate[...]
> >
> > How i can do? i have seen that the package  <<Calculus`Integration` seem
do
> > the integration of piecewise functions in right way, but i have found
> > nothing about differentiation.
> >
> > Someone can help me?
> >
> > Thank and S O R R Y for my ridiculous english
> >
> > Riccardo Piovosi
> >
> > Florence Italy
>


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