From 2006 the course on nonlinear modelling and chaotic behaviour has been taken over by Professor Michael F. Barnsley. See below for information about my book "Exploring Chaos" and the associated "Chaos for Java" software, or follow this link to go directly to the website.
I am currently developing mathematical algorithms and associated software for the restoration of sound files captured from Vinyl (LP) and shellac (78) records and from other sources, such as tape. Information may be found at this link.
Since retiring my principal research interest has been nonlinear dynamics and chaos. I have taught the subject both at undergraduate level and in a graduate summer school, I have revised my book "Exploring Chaos: theory and experiment" for a paperback edition, and also extensively rewritten and extended the accompanying software "Chaos for Java". However, I have also found time to write a new edition of my book "Integral Transforms and their Applications".
Previous research areas include
Exploring Chaos 

"Exploring Chaos: Theory and Experiment", is published by Perseus Books, in hard cover. It uses only elementary mathematics; there are no theorems or proofs. The 246 pages include 179 student exercises and over 100 figures. With the exception of a few line drawings, the latter were produced with "Chaos for Java"; many of the exercises involve experiments using it.  
Exploring Chaos is an ongoing project integrating special purpose software with an undergraduate text book on nonlinear dynamics and chaos. I have been developing the software for some years, for use in the department. It is also extensively linked to the book. Click here to go to the website. 
Integral Transforms 

"Integral Transforms and their Applications", is published by Springer, in hard cover. The first edition appeared in 1977, as volume 25 of the series "Applied Mathematical Sciences". The second (revised) edition, and a translation, appeared a few years later. The third edition is extensivly revised and expanded. It was published in 2001, as volume 41 of the series "Text in Applied Mathematics".  
The book is an introduction and reference for the applications of integral transforms to a wide range of common mathematical problems. Emphasis is placed on the development of techniques and on the connection between properties of transforms and the kinds of problems for which they provide tools. Over 400 problems accompany the text, illustrating areas of applications. The third edition has been substantially updated, extended, and reorganized. The book is intended for advancedlevel students and researchers working in mathematics and its applications. The table of contents may be downloaded here. 
Encyclopaedia of Nonlinear Science 

"The Encyclopaedia of Nonlinear Science", edited by Alwyn Scott, is published by Routledge. It has more than four hundred essays arranged alphabetically. It covers subjects such as chaos and turbulence in addition to the formation (emergence) and dynamics of coherent structure (solitons, nerve impulses, shock waves, tornados, and so on). Entries describe basic phenomena that arise in mathematics; theoretical and applied physics; chemistry; physical chemistry; electrical, chemical, and mechanical engineering; atmospheric and earth sciences; biology; economics; and neuroscience; among several others.  
Entries written by myself, on period doubling and integral transforms, may be downloaded here. Copyright rests with the publisher. The copies are provided, with the publisher's permission, as samples for personal use. 
Department of Mathematics
Mathematical Sciences Institute
Australian National University
Canberra ACT 0200
Australia
+61 6125 2915 (phone)
+61 6125 4984 (fax)
email to Brian.Davies@anu.edu.au