Functional Analysis

3 credits · Graduate

This advanced course deals with analysis on structures varying from metric spaces to normed and Hilbert spaces. Topics include the contraction mapping principle, applications of fixed- point theorems to differential equations, bounded linear operators between normed vector spaces, Banach spaces, duality, Riesz representation theorem, and compact linear maps and their spectra. The course also covers the Fourier transform and shows some of its applications in thermodynamics and diffusion. Prerequisite(s): Permission of the instructor Preclusion(s): MATH 400-3, MATH 402-3, MATH 600-3