Elementary Partial Differential Equations

The mailing list for the course is AM505b@uwo.ca. You can view this list at this ITS site.

Here are some worksheets for the lecture on Monday February 6. (Right click and "save as"). The worksheets work in Maple 9.5.

1. An Introduction to the method of characteristics
2. A breaking wave

This assignment is somewhat open-ended, more analysis than computation, but there is some computation for those so inclined. Make whatever assumptions you need to make progress.

Worksheet and .mpl source for Wed Jan 26 lecture. Wade Cherrington was right when he suggested looking at the energy as a means to understanding the nonlinarity vs numerics problem.

wavexplore.mws

First.mpl

Various old notes from 1998

Integral Equations Lecture: tex, ps, pdf, Maple worksheets

1. inteq.tex
2. colinteq.ps Colour postscript
3. colinteq.pdf Colour pdf
4. intsol1.mws examples of using IntSolve
5. intsol.mws A brain-dead collocation example (it works but it's just for pedagogy )

Notes

Solitons

Recreation of the original "wave of translation"

Soliton home page (with movies)

A Maple animation of a solitary wave and of a two-soliton interaction from an exact solution in Drazin and Johnson.

The Maple V Release 5 worksheet that generated those pictures

February 12, 1998

February 5, 1998.

HTML Form

January 29, 1998.

January 22, 1998

PDF form. For some reason (maybe I don't know how to distill postscript properly) this .pdf form is very ugly. But it is readable at a high enough magnification. If you need to get Adobe Acrobat Reader you can get it free, by clicking on this button

PostScript form

DVI form

The only significant "in-class" addition to these notes was that I gave Perron's Paradox as well:

Let N be the largest integer. Then if N > 1, it follows that N*N > N*1 and hence > N, which is impossible by hypothesis. Therefore N = 1.

The purpose of this paradox is to demonstrate that existence assumptions can get us into trouble, even if we later calculate an answer. That is, it is possible to calculate an incorrect answer merely on the flawed assumption that an answer exists.