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Re: Piecewise functions definition and usage
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24125] Re: Piecewise functions definition and usage
*From*: Brian Higgins <bghiggins at ucdavis.edu>
*Date*: Wed, 28 Jun 2000 02:11:45 -0400 (EDT)
*References*: <8j9ddk$50v@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Viorel, You may want to use the UnitStep function to define your
discontinuous function:
In[20]:=f2[x_] = Sqrt[1 - ((x - 3)/10)^2]*(UnitStep[x + 7] -
UnitStep[x - 13])
In[22]:=Integrate[f2[x], {x, -14, 14}]
Out[22]=5*Pi
Cheers,
Brian
In article <8j9ddk$50v at smc.vnet.net>,
Viorel Ontalus <vio2 at mail.lehigh.edu> wrote:
> It seems I got into an area where Mathematica has some
problems, and I
> hope somebody can give me a hint on how to go around these
problems.
>
> 1. I am trying to define a piecewise function and do some
computations
> with it. When I integrate mathematica does not behave. Here is
an simple
> example you can run and see what I am talking about
>
> Clear[f,x}
> f[x_] := Sqrt[ 1- ( (x-3)/10)^2 ] /;
> Abs[x-3]<10
> f[x_] := 0 /;
> Abs[x-3]>3 ; (*this is a very simple piecewise function but
one
> must be sure the Sqrt is from a positive # )
>
> NIntegrate[f[x],{x,-1,17}] (* Here Mathematica goes nuts !!!*)
>
> Of course it gives an answer but if your program is more
complex, then
> you never get an answer !!
> ( I tried to make the upper limit a variable etc !!)
> Does anybody know how to avoid the error , or non convergence
messages I
> get !!
>
> 2. For fun I tried the only reference from the book on piecewise
> functions:
> If[Abs[x-3]<10, f[x_]:=Sqrt[1- ( (x-3)/10)^2 ] , f[x_]:=0 ]
>
> This definition does not work !!
>
>
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