Metric spaces. Open sets and closed sets. Limit points. Completeness. Compactness and connectedness. Functions on metric spaces. Normed linear spaces. Fixed-point theorem. Functions of several variables. Implicit and inverse function theorems. Additional topic includes Riemann mapping theorem.
Intended Learning Outcomes
CILO-1: Know the properties of continuous functions on metric spaces.
CILO-2: Understand the basic properties of metric spaces.
CILO-3: Understand and be able to compute integrals in vector fields.