- Thread starter
- #1

#### GreenGoblin

##### Member

- Feb 22, 2012

- 68

$y=2uv$

Show the lines in the u,v plane where x and y are constant? (what?)

Is this a valid change of coordinate on the whole x,y plane? (what?)

By letting u = rcost, v=rsint, show that $x=r^{2}cos(2t), y=r^{2}sin(2t)$. Hence show that the map is 2 - 1 (what?) and show that the change of coordinates maps the upper half plane to the whole plane?

Verify that (d(x,y)/d(u,v))(d(u,v)/d(r,t)) = d(x,y)/(d(r,t) (isn't this just basic crossmultiplying?) and find d(r,t)/d(x,y)

So, how do I do this and how do you do these derivatives where its just got two variables? What is d(x,y)/d(u,v) mean?