METHODS OF APPLIED MATHEMATICS-2

MATH 719

Classical theory of partial differential equations, together with an introduction to the modern theory based on functional analysis. Familiarity with basic measure theory (e.g.MATH 629or721) or concurrent registration inMATH 721is strongly recommended.

MATH 703

Study of the linear algebraic structure underlying discrete equilibrium problems. Boundary value problems for continous equilibria: Sturm-Liouville equations, Laplace's equation, Poisson's equation, and the equations for Stokes flow. Contour integration and conformal mapping. Applications of dynamics leading to initial value problems for ODEs and PDEs. Green's functions for ODEs and introduction to asymptotic methods for ODEs, e.g. WKB analysis. Separation of variables and eigenfunction expansions for linear PDEs. Examples from physics and engineering throughout. Knowledge of undergraduate linear algebra, analysis and complex analysis is strongly recommended.

MATH 322

Sturm-Liouville theory; Fourier series, including mean convergence; boundary value problems for linear second order partial differential equations, including separation of variables and eigenfunction expansions.

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.

MATH 720

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