Abel's Theorem in Complex analysis

I am taking Complex Analysis class and I am trying to prove Abel's theorem. a). I want to prove that if sum of a_n(z-a)^n have radius of convergence 1 and if the sum a_n converges to A then lim (r -> 1- ) of the sum (a_n r^n) = A. ( I believe z here is a complex number). b). Using Abel's theorem, prove that log2 = 1 - 1/2 + 1/3 - ...

Exponential

(See attached file for full problem description with symbols and equations) --- Prove that by applying the following Corollary: Corollary. If and are analytic on a region then iff has a limit point in . ---

Potential flow theory

(See attached file for full problem description) --- The transformation (see attached) transforms a circle with unit radius... ---

Potential flow theory

(See attached file for full problem description) --- The complex potential for a flow over a body is given by... ---

Potential flow theory

(See attached file for full problem description) --- Find the resultant velocity vector induced at point A... ---