[Related concepts: Inverse mapping theorem, transformations and coordinate systems]
1) For each of the following transformations (u,v) = f(x,y), (i) compute det Df, (ii) find formulas for the local inverses of f when they exist.
a) u=x^2, v=y/x
b) u=(e^x) cos y, v=(e^x) sin y
I got...