Seems like it should be simple enough, but I haven't made any real progress....
Construct a bijective conformal mapping from the region below the parabola $y=x^2$ to the upper half plane.
My first thoughts are to map $y=x^2$ or looking around online it seems smart to map to the disk, which is something I am familiar with.... but how would I go about doing this? Any ideas?
I also thought to convert to polar coordinates and work with those, but It really just got uglier from there.
Much Thanks!
