Faculty of Engineering and Science
The International Doctoral School of Technology and Science

PhD Course

Web page updated May 30, 2006 .

Below are links to files used in demonstrations during the lectures

Maple file illustrating the derivation of finite difference formulas through interpolation.
Maple file showing the structure of the periodic spectral differentiation matrix.
Maple file computing the derivatives needed in the infinte spectral differentiation formula.
Maple file computing the derivatives needed for the periodic spectral differentiation matrix.
Maple file illustrating Exercise 3.1 from [T].
Maple file illustrating the location of the Chebyshev points.
Maple file ilustrating the difference between interpolation based on the equidistant points and Chebyshev points. The function being approximated is the famous one called the Runge function.
Matlab toolbox to compute pseudospectra can be downloaded from here.

Here are some m-files with examples and exercises concerning pseudospectra. The files contain as comments some explanations.

A set of Lecture Notes on Complex Analysis can be found here. They are intended for mathematics students (third semester), but the statements of the results should be accessible without studying the proofs in detail.
Notes on Chapter 5 in Trefethen's book can be found here. The error estimate in polynomial approximation is derived, as is the error estimate for spectral differentiation based on the Chebyshev points.

Updated May 30, 2006, by Arne Jensen.