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Piecewise functions definition and usage
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24098] Piecewise functions definition and usage
*From*: Viorel Ontalus <vio2 at mail.lehigh.edu>
*Date*: Tue, 27 Jun 2000 00:51:54 -0400 (EDT)
*Organization*: Lehigh University
*Sender*: owner-wri-mathgroup at wolfram.com
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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