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 * Why integral equations?
  * Reminder: Condition Number
  * Reminder: Catastrophic cancellation
  * Weaknesses of PDE discretization approach
   
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== Numerics Intro == == Lecture N: Quadrature ==
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 * Quadrature
 * SVD
 * Condition Number
 * Trapezoidal rule
 * Spectral accuracy vs finite smoothness (a la ATAP)

== Lecture N: Types of Multipoles ==

 * Taylor multipoles
 * Separation-of-variables multipoles
 * Particle-based multipoles: SVD, ID

Detailed syllabus

Lecture 1

  • Syllabus-ish
    • Homework 60%
    • Final project 40% (report)
  • Why integral equations?
    • Reminder: Condition Number
    • Reminder: Catastrophic cancellation
    • Weaknesses of PDE discretization approach
  • Intuition: what is a...
    • layer potential

Lecture 2: Basics from Functional Analysis

  • Banach space
  • Hilbert space
  • Operator notion
  • continuity
  • Compact operator
  • Fredholm alternative
  • Riesz-Schauder theory

Homework:

Lecture 3: Integral equations, a zoology

  • ODEs and Volterra integral equations
  • ODEs and Volterra integral equations

Lecture N: Quadrature

  • Trapezoidal rule
  • Spectral accuracy vs finite smoothness (a la ATAP)

Lecture N: Types of Multipoles

  • Taylor multipoles
  • Separation-of-variables multipoles
  • Particle-based multipoles: SVD, ID

Teaching/IntegralEquationsFall2013/DetailedSyllabus (last edited 2013-08-18 03:42:48 by AndreasKloeckner)