18.307 Integral Equations

As taught in: Spring 2006

Figure showing temperature regions around a plate.

Temperature profile around a plate (red: hot, to blue: cold), which is found via a singular integral equation. (Courtesy of Dr. Jaehyuk Choi. Used with permission.)

Level:

Graduate

Instructors:

Dr. Dionisios Margetis

Course Description

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.