||Metric spaces, point-set topology, Cauchy sequences and completeness, compact metric spaces. Continuous functions on metric spaces, continuity and connectedness, continuity and compactness. Sequences and series of functions, pointwise and uniform convergence. Uniform convergence and continuity, integration, and differentiation. Power series and real analytic functions. Inner products on periodic functions, L^2 convergence of Fourier series and Plancherel's Theorem.