Fall 2024

4512: Differential Equations with Applications

MWF 10:10 AM - 11:00 AM, VinH 1

In this course, we will study differential equations and their role as models in applied sciences. We will be able to solve some types of equations (mainly linear ones) explicitly to some extent, but for nonlinear equations explicit solutions are seldom available. In such cases, we will use qualitative analysis to understand the behavior of the solutions.

Text: Differential Equations and their Applications by Martin Braun (4th edition).

Syllabus, assignments, and other relevant information for this course will be posted on Canvas.


8583:  Theory of Partial Differential Equations

MWF 02:30-03:20, VinH 301

This is the first part of a year-long graduate course in partial differential equations (PDEs). After some introductory overview, we will discuss a few  results concerning some general classes of PDEs (existence/uniqueness for analytic PDEs, transform techniques in constant coefficients PDEs, first-order PDEs). Our study will then be divided into several parts dealing with different types of equations. You will gain some intuition about PDEs of elliptic, parabolic, and hyperbolic types by examining their archetypes: Laplace, heat, and wave equations. Then, proceeding toward the theory of general linear second order PDEs of elliptic, parabolic, and hyperbolic types, we will cover the basic theory of Sobolev spaces.      

Syllabus, assignments, and other relevant information for this course will be posted on Canvas.