PARTIAL DIFFERENTIAL EQUATIONS

MATH 821

Topics in partial differential equations and real analysis.

MATH 721

Real analysis concentrating on measures, integration, and differentiation and including an introduction to Hilbert spaces. Knowledge of undergraduate analysis (e.g. the sequenceMATH 521and522) is strongly recommended.

MATH 322

Sturm-Liouville theory; Fourier series, including mean convergence; initial and boundary value problems for linear second order partial differential equations, including separation of variables and eigenfunction expansions; fundamental solutions and Green's functions in multiple dimensions.

MATH 720

Linear elliptic, parabolic and hyperbolic equations, continuing with calculus of variations and then nonlinear initial value problems.

MATH 619

A rigorous introduction to the theoretical underpinnings of the basic methods and techniques in the modern theory of PDEs. It is aimed at math majors, but will also be useful to some students in the sciences, engineering and economics who feel the need for a deeper understanding of the theory of PDEs. The emphasis is on the exposure to a number of different methods of solution of PDEs and their connection to physical phenomena modeled by the equations. The goals include both learning to solve some basic types of PDEs as well as to understand the motivation behind and inner workings of the techniques involved.