Differences between revisions 2 and 3
 ⇤ ← Revision 2 as of 2013-08-18 03:34:58 → Size: 591 Editor: AndreasKloeckner Comment: ← Revision 3 as of 2013-08-18 03:42:48 → ⇥ Size: 927 Editor: AndreasKloeckner Comment: Deletions are marked like this. Additions are marked like this. Line 10: Line 10: * Why integral equations?  * Reminder: Condition Number  * Reminder: Catastrophic cancellation  * Weaknesses of PDE discretization approach Line 12: Line 17: Line 30: Line 36: == Numerics Intro == == Lecture N: Quadrature == Line 32: Line 38: * 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

• 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)