MATH 600 - Real Analysis

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Review of properties of (usual) norm and inner product in Rn, countable and uncountable sets. Basic ideas of metric spaces. Compact, connected, and complete metric spaces, continuous and uniformly continuous functions on metric spaces. Fixed points and Banach contraction principle. Uniform convergence of sequences and series of functions, term-by-term differentiation and integration. Power series and radius/interval of convergence. Arzela-Ascoli theorem. The weierstrass approximation theorem on a compact interval. Differentiation in Rn. Inverse and implicit function theorems.
Prerequisite: Prerequisite: MATH 301.