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...