Re: Piecewise functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg23196] Re: [mg23119] Piecewise functions*From*: Matt.Johnson at autolivasp.com*Date*: Mon, 24 Apr 2000 01:12:05 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

An- You can define a piecewise function by use of UnitStep[x]... Suppose I have 3 functions: x^2 for x<=0 x for 0<=x<=10 -x+20 for x>=10 Then they can be defined with UnitStep[]: fun1[x_] := x^2*UnitStep[-x]; fun2[x_] := x*(UnitStep[x] - UnitStep[x - 10]); fun3[x_] := (-x+20)*UnitStep[x - 10]; Then, we can combine these into one function and plot to check it: fun[x_] := fun1[x] + fun2[x] + fun3[x]; Plot[fun[x], {x, \(-10\), 20}]; The UnitStep function also allows integration: In[31]:= Integrate[fun[x], x] Out[31]= x^3/3 + 20(-10 + x) UnitStep[-10 + x] - 2(-50 + x^2/2) UnitStep[-10 + x] + 1/2 x^2 UnitStep[x] - 1/3 x^3 UnitStep[x] -matt An Le <an_le at brown.edu> on 04/19/2000 12:30:49 AM Subject: [mg23196] [mg23119] Piecewise functions Can someone send me some notebook and package files to do piecewise functions? I can't seem to be able to do it with mathematica. The only thing i get close to is using the Which[] function, but I can't integrate with that function. Thanks...