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* A Gentle Intro: Calculus/Linear Algebra/Python warmup  * A Gentle Intro: Linear Algebra/Numerics/Python warmup 
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* Leslie Greengard  * [[https://cs.nyu.edu/courses/spring12/CSCIGA.2945001/index.htmlLeslie Greengard]] 
Integral Equations and Fast Methods
Class Time/Location 
TBD 
Instructor 

Office 
TBD 
Office Hours 
TBD 
Class Webpage 

Email Listserv 
Contents
Description
This class will teach you how how (and why!) integral equations let you solve many common types of partial differential equations robustly and quickly.
You will also see many fun numerical ideas and algorithms that bring these methods to life on a computer.
What to expect
 A Gentle Intro: Linear Algebra/Numerics/Python warmup
 Some Potential Theory
 The Laplace, Poisson, Helmholtz PDEs, and a few applications
 Integral Equations for these and more PDEs
 Ways to represent potentials
 Quadrature, or: easy ways to compute difficult integrals
 Tree codes and Fast Multipole Methods
 Fun with the FFT
 Fast Randomized Linear Algebra (if time)
Updates
 Month 1, 2013
 Class starts on MONTH DAY, 2012, from XXXXpm. We've also been assigned a room. We will be meeting in XXX. See you then!
Grading/Evaluation
This isn't final yet.
If you will be taking the class for credit, there will be
 Weekly homework for (roughly) the first half of the class (50% of your grade)
A more ambitious final project, which may be inspired by your own research needs (50% of your grade) (also see /ProjectGuidelines)
If you're planning on auditing or just sitting in, you are more than welcome.
Homework
Material
Books
These books cover some of our mathematical needs:
Foundations of Potential Theory by Kellogg
Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems by Nédélec
Integral Equations by Hackbusch
There really aren't any books to cover our numerical and algorithmic needs.
So, unfortunately, there isn't one book that covers the entire class, or even a reasonable subset. It will occasionally be useful to refer to these books, but I would not recommend you go out and buy them just for this course. I will make sure they are available in the library for you to refer to.
Source articles
Because of the (no)book situation (see above), I will post links to the research articles underlying the class here.
Related classes elsewhere