Real and Complex Analysis
This course is a study in modern real and complex analysis. Topics from real analysis include: measure theory and integration; Banach, Hilbert, Lp -spaces; uniform boundedness principle, the open mapping theorem and closed graph theorem. After a review of analytic functions, harmonic functions, the residue theorem and the maximum modulus principle, additional topics in complex analysis include: Riemann mapping theorem, analytic continuation, Poisson's integral formula and Dirichlet's problem. Applications include partial differential equations.