Introduction to the theory of power series. Differentiability of power series. Green's Theorem in complex form. The proof of Green's Theorem. Liouville's theorem, the Fundamental Theorem of algebra and Morera's theorem.
Every holomorphic function is analytic.
Open mapping Theorem and the argument principle. The residue theorem, evaluation of indefinite integrals and infinite sums. Schwarz's Lemma and Rouchet's Theorem. Conformal mappings of the disc and locating roots of polynomials. A.5.2.1 Partial fraction decomposition.