Applied Analysis

Catalog description

Convergence sequences and series of functions; metric space topology, compactness, completeness and the Ascoli-Arzela Theorem; Contraction Mapping Principle, Implicit Function Theorem; intro to Lebesgue integration leading to $L^p$-spaces; properties of Hilbert spaces, Fourier transform. Students should have knowledge of linear algebra, multivariable calculus, and analysis at the undergraduate level.