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docnet

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- Homework Statement
- Find the image of the unit disk under this transformation.

- Relevant Equations
- Please see below.

Hi all,

I am trying to figure out a way to simplify this problem to give the image of the map. I have not seen this function before and I am having trouble figuring out what the image should come out as.

I have tried graphing u and v separately as a function of x and y in

*R*and both surfaces go to infinite z within the domain of our unit disc. This means u and v go to infinity in the UV plane.

^{3}What we know is the image exists for positive u and for positive and negative v.

The best and neatest solution would be obtained by manipulating u and v to give

*x*

^{2}+ y^{2}= 1I tried computing simple choices like

*u*that do not yield a solution.

^{2}+v^{2}Does anyone know what the image is off the top of their head?

Thank you.