Analysis II

3 credits · Undergraduate Programs

An intermediate course in the theory of metric spaces and the continuous functions that act on them: metric spaces and normed vector spaces; complete metric spaces and the Baire category theorem; continuous functions on compact metric spaces and uniform convergence; the contraction mapping principle and applications; theorems of Stone-Weierstrass and Arzelà-Ascoli; differentiability on Euclidean spaces and the implicit function theorem. Prerequisite(s): Mathematics 367; and Mathematics 311; and Mathematics 335 or 355.