Integral Equations and Fast Algorithms

Course number: MATH-GA 2011.002
Semester: Fall 2017
Time & Location: Thurs, 1:25pm - 3:15pm in WWH 512
Instructor: Mike O'Neil (oneil@cims.nyu.edu)
Office hours: By appointment
Course description

This course will be an introduction the theory and application of integral equations in classical mathematical physics, as well as the numerical methods required for their efficient and accurate solution. These numerical methods include quadrature for singular functions, analysis-based fast algorithms (e.g. fast multipole methods), iterative and fast-direct solvers (for the resulting dense linear systems). Methods from potential theory, applied analysis, functional analysis, numerical linear algebra, complex analysis, and asymptotic analysis are central to the construction of almost all of these algorithms.

Materials

There is no one textbook for this course. Instead, there will be continually updated lectures notes available. These lecture notes will contain many useful references for each of the topics and algorithms covered in class. As they become relevant, original journal articles and textbooks will be listed below in the table of lecture topics.

Relevant code examples will be posted on gitlab.com/oneilm/integralequations.

Grading

The grades in the course will be determined by a few homework exercises and a final project.

Announcements

Important information for the course will appear below as necessary.

  • Class on September 7th is CANCELLED. The first class on September 14
Schedule

Below is an updated list of lecture topics along with any documents that were distributed, or relevant code.

Date Topics Materials
September 7 No class - cancelled.
September 14 Overview, electrostatics and the Laplace equation
September 21
September 28
October 5
October 12
October 19
October 26
November 2
November 9
November 16
November 23 No class - Thanksgiving.
November 30
December 7
December 14