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 !! > > Sent via Deja.com http://www.deja.com/ Before you buy.