Re: Integrating Conditionals/piecewise cont. functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg26228] Re: [mg26221] Integrating Conditionals/piecewise cont. functions*From*: BobHanlon at aol.com*Date*: Wed, 6 Dec 2000 02:16:16 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

vp[x_, n_] := UnitStep[x - n] - 2*UnitStep[x - n - 1] + UnitStep[x - n - 2]; Plot[vp[x, 3], {x, 2, 6}]; Table[Integrate[vp[x, m]*vp[x, n], {x, Min[m, n], Max[m, n] + 2}], {m, 5}, {n, 5}] Bob Hanlon In a message dated 12/3/00 6:26:06 PM, georgepburdell at hotmail.com writes: >I am trying to do some simplified finite elements that simply requires >the >integration of some roof functions (i.e. piecewise continous functions >that >are 0 everywhere except where they ramp up and then down in a specified >domain). I was hoping that I could do everything symbolically, but >Mathemtica refuses to integrate every conditional I give it. I can get >it to >do the numerically, but it comes with baggage. This is what I have right >now: > >These are roof functions differentiated > >Piecewise continuous >b'[x_, n_] := > Which[x < n, 0, n <= x <= n + 1, 1, n + 1 < x < n + 2, -1, x >= n + 2, >0] > >Another way to look at it >v'[x_, n_] := 0 /; x < n >v'[x_, n_] := 1 /; n <= x <= n + 1 >v'[x_, n_] := -1 /; n + 1 < x < n + 2 >v'[x_, n_] := 0 /; x >= n + 2 > >I want to simply do this... > >Integrate[v'[x,m] v'[x,n]] for m=n=1...5 (or something) >