RE: Define a function
- To: mathgroup at smc.vnet.net
- Subject: [mg34595] RE: [mg34556] Define a function
- From: "David Park" <djmp at earthlink.net>
- Date: Wed, 29 May 2002 02:45:09 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Michael,
The best method for defining piecewise functions is to use UnitStep.
f[x_] := x(UnitStep[x - 10] - UnitStep[x - 20]) + x/2UnitStep[x - 20]
This will not only plot...
Plot[f[x], {x, 0, 30}];
but you can also do things like integrate.
g[x_] = Integrate[f[x], x]
(-(1/4))*(-400 + x^2)*UnitStep[-20 + x] +
(-50 + x^2/2)*UnitStep[-10 + x]
Plot[g[x], {x, 0, 30}];
The Mathematica Book, which has not really been updated properly to reflect
the UnitStep function often leads users to using conditional definitions.
Clear[f]
f[x_] /; x < 10 := 0;
f[x_] /; 10 <= x <= 20 := x;
f[x_] /; 20 < x := x/2;
This works for plotting...
Plot[f[x], {x, 0, 30}];
but won't integrate or perform other calculus functions.
Integrate[f[x], x]
Integrate[f[x], x]
So, the UnitStep method is far superior.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
> -----Original Message-----
> From: Michael Popp [mailto:popp.michael at gmx.at]
To: mathgroup at smc.vnet.net
> Sent: Monday, May 27, 2002 1:17 AM
> Subject: [mg34595] [mg34556] Define a function
>
>
> Hello
>
> I want to define a function in Mathematica. But just f[x_]:=... does not
> work, because I have to define different functions for different ranges of
> the variable x.
> For example:
>
> x < 10: f(x) = 0
> 10 < x < 20: f(x) = x
> 20 < x: f(x) = x/2
>
> How to do this?
>
> Thanks, greetings
> Michael
>
>
>
>