Mathematics: Partial Differential Equations

Classification of equations, linear equations, first order equations, second order elliptic, parabolic, and hyperbolic equations, uniqueness and existence of solutions. Prerequisite: Knowledge of differential equations required.

Prereq: Differential Equations; Open to Degree and PACE students

This is a graduate-level course on partial differential equations. It covers classical topics on partial differential equations, such as the solution methods for the heat equation, wave equation and Laplace equation in one and higher spatial dimensions, Sturm-Liouville eigenvalue problems, the method of characteristics for quasilinear wave equations, the Fourier and Laplace transform methods, and so on. Physical motivations for these partial differential equations will also be provided. This course will build a solid mathematical foundation for solving partial differential equations in physical and engineering applications. It will also build mathematical maturity for students to take other graduate-level applied mathematics courses such as Nonlinear Partial Differential Equations (Math 6249). This course is intended for graduate students and senior undergraduate students in mathematics, physics and engineering.

The pre-requisite for this class is Math 3230 (Ordinary Differential Equations). Knowledge of Math 5230 (Advanced ODEs) is helpful but not required. This course is in in-person lecture format. The textbook for this class will be communicated to the registered students before the spring semester starts.

There will be homework (almost weekly), two in-class exams and a final project. Grading will be based on all these materials.