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 |

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.

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.

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

Important information for the course will appear below as necessary.

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

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 |