PASI II header

Wavelets and Partial Differential Equations

Martin J. Mohlenkamp (Department of Mathematics, College of Arts & Sciences, Ohio University)

A course presented at the II Pan-American Advanced Studies Institute in Computational Science and Engineering, Universidad Nacional Autónoma de Honduras, Tegucigalpa, Honduras, June 14-18, 2004.

Course Description

In this course we will discuss the basics of wavelets. Including multiresolution analysis, lifting techniques, and basic applications to data compression, denoising, and signal and image processing. We will discuss the interplay between wavelets and differentiation. In particular we will discuss efficient representation in terms of wavelets of derivatives and products, and how to handle boundary terms as well as irregular data. These are all cornerstones of many non-linear PDE solvers.

Course Outline

The official course outline, which was created (by Cristina Pereyra) some months earlier, is:
Lecture 1: Time/Frequency Analysis
Lecture 2: Fast Algorithms and Applications
Lecture 3: Main Characters
Lecture 4: Variations over a Theme
Lecture 5: Applications to Signal/Image Processing
The outline of what was actually taught is:
Day 1: Background
Lecture on:
Day 2: Basic Wavelets
Lecture on: followed by demonstrations in the computer lab using the Matlab wavelet toolbox.
Day 3: General Wavelets
Lecture on:
Day 4: Multiwavelets and PDEs
Lecture on:
Day 5: Finale

Course Materials

Cristina Pereyra and I produced a set of lecture notes (.pdf).

Some slides used were from a tutorial on Wavelets and their Applications (.pdf) that I gave in 2002.

There is also a lot of freely available information on the web. Here is a selection of general resources:

Martin J. Mohlenkamp
Last modified: Sun Jul 4 14:12:50 EDT 2004