My colleague and good friend Peter Chapman passed away on the 8th February 2008. After completing his Ph. D. at the Department of Aeronautical Engineering at the University of Sydney he worked at the University of Toronto for 9 years, and then he shifted to UWA where he remained until he retired. He continued working until his death. He left behind a mathematical legacy of published and unpublished material. More details of Peter's professional life can be found in his (academic) obituary below, and a list of his published work is presented in `Publications'.
Peter truly enjoyed mathematics, science and engineering for their own sake. He read broadly and always felt the need to establish or verify results in his own idiosyncratic way. He was not at all concerned with publication, so much of his academic legacy is not publicly available. In todays academic world this would be regarded as an unacceptable luxury. In any case this has meant that much of his work remains unknown to the broader mathematical community. His widow, Connie, and I have attempted to make his material generally available by collecting together his files.
Peter's primary mathematical interest was in asymptotics and he frequently transformed problems or specific equations arising out of engineering and science in a way that enabled him to use these techniques to extract results and thus expose the physics. In many cases the results he obtained were not new and so were not of primary research interest, but his approach certainly led to new insights. As an example of this, Peter explored the quantum mechanics/classical mechanics interface in Quantum Theory and Classical Mechanics, displaying the result that classical mechanics represented an asymptotic limit of the quantum mechanics equations. This work had been done earlier by pioneers in the area but not in the way that Peter did it. His (extensive) notes on this are interesting and of real educational value.In other cases the work certainly was of primary research interest but, as indicated above, Peter's concern was not with publications but with understanding. He felt happy that he now understood the problem in his own way and so moved on. I put his important work Asymptotics and the Helmholtz Equation work in this category. We have briefly described the material here. Peter was a generous character and was in no way possessive about his contributions, however, his family and I would ask colleagues who make use of this unpublished work to acknowledge his contribution.
October 2010.
Oscillatory systems excited by external forces at the natural frequency will result in growing amplitude oscillations (resonance). Usually, however, the resonant forcing is not sustained and the challenge is to determine the amplitude growth that occurs under intermittent natural frequency forcing. Peter points out (by example) that in many circumstances the solution can be represented in integral form so that powerful complex variable and asymptotic methods can be used to extract results. These is an earlier account of Peter's J Aust Math Soc B vols 34, 35 1994 publications.