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)
>

```

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