Real Analysis II
Description
Sequence of functions, uniform convergence, spaces of continuous functions. Dini’s theorem. Uniform convergence and interchanging of the limit operation with differentiation and integration. Series of functions, criteria of uniform convergence (M-test, Abel, Dirichlet). Power-series. Theory of Fourier series. Compactness and connectedness in metric spaces, compact and connected subsets of ℝn.
Division: Pure Mathematics