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MathGroup Archive 2004

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Re: Help: piecewise functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50133] Re: Help: piecewise functions
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 17 Aug 2004 05:00:44 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <cfi96d$4s5$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

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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