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Topic: how to define and analyze function with multiple parts
Replies: 4   Last Post: Apr 20, 2013 5:56 AM

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Murray Eisenberg

Posts: 2,097
Registered: 12/6/04
Re: how to define and analyze function with multiple parts
Posted: Apr 20, 2013 5:55 AM
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Perhaps you have in mind something like the following (for n = 3)?

u1[{x_,y_,z_}]:=3x-4y+z
u2[{x_,y_,z_}]:=10x y z

u[{x_, y_, z_}] :=
Piecewise[{{u1[{x, y, z}], x^2 + y^2 + 3 z^2 <= 1},
{u2[{x, y, z}], x^2 + y^2 + z^3 > 100}}]


On Apr 19, 2013, at 1:17 AM, pjanakir1978@gmail.com wrote:

> Hi, I have a function on the plane that has 2 different formulation for 2 different regions. Let x = (x1, ..., xn). I want to define it as
>
> U(x) = U_1(x) if x is in region 1
> = U_2(x) if x is in region 2
>
> Then I want to analyze such a defined function, like find its max, etc, using NMaximize, or put in some other expressions in place of x, to see behavior of U.
>
> Essentially, how does one define a multipart function, so that we can analyze it in the same way we may analyze a single part function or polynomial?
>
> Thanks.
>
> Prabhu


---
Murray Eisenberg murray@math.umass.edu
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