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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