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|| ''Class Time/Location'' || Wednesday 5:10-7pm, Room 101 Warren Weaver Hall || || ''Class Time/Location'' || TBD ||
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|| ''Class Webpage'' || http://bit.ly/ieq13 ||
|| ''Email Listserv'' || [[http://lists.tiker.net/listinfo/ieq13|Info page]] ||
|| ''Class Webpage'' || http://bit.ly/inteq13 ||
|| ''Email Listserv'' || [[http://lists.tiker.net/listinfo/inteq13|Info page]] ||
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[[attachment:flyer.pdf|Class advertisement]]


|| ''Email Listserv'' || [[http://lists.tiker.net/listinfo/ieq13|Info page]] ||

[[attachment:flyer.pdf|Class advertisement]]
[[attachment:flyer.pdf|Class poster]]
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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 warm-up
 * 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)
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 Month 1, 2013:: Class starts on XXXX 5, 2012, from XX-XXpm. We've also been assigned a room. We will be meeting in XXX . See you then!  Month 1, 2013:: Class starts on MONTH DAY, 2012, from XX-XXpm. We've also been assigned a room. We will be meeting in XXX. See you then!
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 * A more ambitious final project, which may be inspired by your own research needs (40% of your grade) (also see [[/ProjectSubmissionGuidelines]])  * A more ambitious final project, which may be inspired by your own research needs (50% of your grade) (also see [[/ProjectGuidelines]])
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 * These books cover some of our mathematical needs:

 * [[http://books.google.com/books?isbn=0486601447|Foundations of Potential Theory]] by Kellogg
 * [[http://books.google.com/books?isbn=9780387951553|Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems]] by Nédélec
 * [[http://books.google.com/books?isbn=3764328711|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.
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 * [Shidong Jiang](http://web.njit.edu/~jiang/math707.html)
 * [Alex Barnett](http://www.math.dartmouth.edu/~m126w12/)
 * [Shravan Veerapaneni](https://sites.google.com/a/umich.edu/math-671-fast-algorithms/)
 * [[http://web.njit.edu/~jiang/math707.html|Shidong Jiang]]
 * [[http://www.math.dartmouth.edu/~m126w12/|Alex Barnett]]
 * [[https://sites.google.com/a/umich.edu/math-671-fast-algorithms|Shravan Veerapaneni]]
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 * [Gunnar Martinsson](http://amath.colorado.edu/faculty/martinss/main_teaching.html)
 * [Jianlin Xia](http://www.math.purdue.edu/~xiaj/teaching/692.11s/)
 * [Francesco Andriulli](http://public.telecom-bretagne.eu/~fandriul/teaching.html)
 * [[http://amath.colorado.edu/faculty/martinss/Teaching/APPM5720_2011s/index.html|Gunnar Martinsson]]
 * [[http://www.math.purdue.edu/~xiaj/teaching/692.11s/|Jianlin Xia]]
 * [[http://public.telecom-bretagne.eu/~fandriul/teaching.html|Francesco Andriulli]]
 * [[http://cims.nyu.edu/%7Etygert/gradcourse/survey.pdf|Mark Tygert]]

=== Online resources ===

 * The [[http://dlmf.nist.gov|Digital Library of Mathematical Functions]]
 * [[http://people.math.sfu.ca/~cbm/aands/|Abramowitz and Stegun: Handbook of Mathematical Functions]]

Flyer thumbnail

Integral Equations and Fast Methods

Class Time/Location

TBD

Instructor

Andreas Kloeckner

Email

kloeckner@cims.nyu.edu

Office

TBD

Office Hours

TBD

Class Webpage

http://bit.ly/inteq13

Email Listserv

Info page

Class poster

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 warm-up
  • 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 XX-XXpm. 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:

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.

Online resources

Teaching/IntegralEquationsFall2013 (last edited 2014-01-23 02:26:25 by AndreasKloeckner)