Media Summary: Finishing up the topological preliminaries: "distance lemma" (positive distance between a compact set and a closed set); uniform ... Basic topology review: open sets, open sets and set operations, limits, uniqueness of limits, limits and arithmetic, continuity. Mean Value Property of analytic functions; local maximum modulus principle; maximum modulus principle; existence of harmonic ...
Math 135 Complex Analysis Lecture - Detailed Analysis & Overview
Finishing up the topological preliminaries: "distance lemma" (positive distance between a compact set and a closed set); uniform ... Basic topology review: open sets, open sets and set operations, limits, uniqueness of limits, limits and arithmetic, continuity. Mean Value Property of analytic functions; local maximum modulus principle; maximum modulus principle; existence of harmonic ... Zeroes of analytic functions: zeroes of finite order; isolation of zeroes; identity theorem (analytic functions that agree on a set with ... Definition of conformal mappings; analytic implies conformal; Cauchy-Riemann equations are satisfied by analytic functions; ... Analytic continuation: function element; direct analytic continuation; global analytic function; analytic continuation. Analytic ...
Power series; prototypical power series: geometric series; lim sup and lim inf; Abel-Weierstrass theorem on the existence of a ... Inverse function theorem (for analytic functions); harmonic functions; harmonic conjugates; (example of) non-existence of a ...
