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