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← Revision 3 as of 20130818 03:42:48 ⇥
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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 * Separationofvariables multipoles * Particlebased multipoles: SVD, ID 
Detailed syllabus
Lecture 1
 Syllabusish
 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
 RieszSchauder 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
 Separationofvariables multipoles
 Particlebased multipoles: SVD, ID