Double Integral : Disc - By changing variables to polar coordinates evaluate the integral , where
And ,
i.e., the disc of radius 3 centred at the origin.
Please see the attached file for the fully formatted prob ...
Analytic - Suppose that f is analytic in the disc |z|<1, that f(0) = f'(0) = 0 and that |f(z)| ≤ 1 for all z in the disc. Show that |f(z)| ≤ |z^2|, for |z|<1.
Hint: Schwarz's Lemma:
Suppose that f ...