RE: RE: Definitions of the functions
- To: mathgroup at smc.vnet.net
- Subject: [mg34993] RE: [mg34977] RE: [mg34963] Definitions of the functions
- From: "DrBob" <majort at cox-internet.com>
- Date: Tue, 18 Jun 2002 02:48:36 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
I think UnitStep would be easier to use if we could define the function
this way:
y2[x_] :=
x UnitStep[-x - 5] + x^2 UnitStep[x + 5]UnitStep[18 - x] +
Sin[x]UnitStep[x - 18]
or
y3[x_] :=
x UnitStep[-x - 5] + x^2 UnitStep[x + 5, 18 - x] + Sin[x]UnitStep[x -
18]
Either of these gives the same function values (except at -5 and 18),
but Integrate doesn't evaluate either of them.
Bobby
-----Original Message-----
From: David Park [mailto:djmp at earthlink.net]
To: mathgroup at smc.vnet.net
Subject: [mg34993] [mg34977] RE: [mg34963] Definitions of the functions
Pawes,
For plotting and arithmetic...
y[x_] /; x < -5 := x
y[x_] /; -5 <= x < 18 := x*x
y[x_] := Sin[x]
Plot[y[x], {x, -10, 30},
PlotRange -> All];
For calculus...
Clear[y];
y[x_] = x(1 - UnitStep[x + 5]) + x*x(UnitStep[x + 5] - UnitStep[x - 18])
+
Sin[x]UnitStep[x - 18] // Simplify
(-x^2 + Sin[x])*UnitStep[-18 + x] +
x*(1 + (-1 + x)*UnitStep[5 + x])
g[x_] = Integrate[y[x], x] // Simplify
(1/6)*(3*x^2 - 2*(-5832 + x^3 - 3*Cos[18] + 3*Cos[x])*
UnitStep[-18 + x] + (325 - 3*x^2 + 2*x^3)*
UnitStep[5 + x])
Plot[g[x], {x, -10, 30},
PlotRange -> All];
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
> From: Pawe³ Ga³ecki [mailto:pmg at wp.pl]
To: mathgroup at smc.vnet.net
>
>
> How do I define a function that is described by different
> formulas depending
> of the interval which the argument is given in????
> For example:
>
> y=x for -inf<x<-5
> y=x*x for -5<=x<18
> y=sin x for all the remaining values of x.
>
>
> Anybody got a clue???
>
> Thanks,
> Pawe³ Ga³ecki
>