Help: piecewise functions
- To: mathgroup at smc.vnet.net
- Subject: [mg50066] Help: piecewise functions
- From: "rik" <rikypi_ALLA_LARGA at libero.it>
- Date: Fri, 13 Aug 2004 05:56:48 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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