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Maths of waves and fields (PHYS 20171)

Lecture summaries Textbooks Boas's book is the one I recommend most strongly for this course. The 2nd and 3rd editions cover the same material, but the sections on Fourier transforms are organised differently. A good alternative (which some people prefer) is the one by Riley, Hobson and Bence. Another useful book is the one by Stephenson. This covers PDE's, Fourier methods (briefly) and their applications to a variety of physics problems, but it assumes you already know about special functions. M. Boas, Mathematical methods in the physical sciences, 2nd or 3rd edition (Wiley) K. F. Riley, M. P. Hobson and S. J. Bence, Mathematical methods for physics and engineering (Cambridge) G. Stephenson, Partial differential equations for scientists and engineers (Imperial College) Note that I am not following exactly the same approach to the material as Boas. The sections of her book referenced in the lectures are the most relevant ones. You may find that the ordering of topics and the choice of physics examples are different in them. Web resources Notes Lecture notes are available (in HTML) for 2C1: Further Mathematical Methods, a very similar course given at UMIST by Niels Walet. Applets and movies There a quite a few applets or movies available on the web which illustrate the ideas in this course. Some of the ones I like best are listed below: Fourier synthesis (with sound) by Tom Huber (Gustavus Adolphus College, Minnesota) Fourier synthesis (with sound) by Fu-Kwun Hwang (National Taiwan Normal University), via a mirror site at Aberdeen Vibrating string by Paul Falstad Vibrating bar and other one-dimensional waves by Paul Falstad. A more general version of the preceding applet. Try the string setup with different boundary conditions (pinned/free and free/free). Rectangular membrane by Paul Falstad Circular membrane by Paul Falstad Rectangular membrane movies by Dan Russell (Kettering University, Michigan) Circular membrane movies by Dan Russell (Kettering University, Michigan) More physics and maths applets and movies Applets by Paul Falstad: a large set of cool applets for waves, acoustics, electromagnetism and quantum mechanics Physlets from WebPhysics at Davidson College Java virtual physics laboratory: a large set of applets on waves, dynamics and other topics by Fu-Kwun Hwang (National Taiwan Normal University), via a mirror site at the University of Aberdeen Acoustics and vibration animations by Dan Russell (Kettering University, Michigan) The living mathematics project at the University of British Columbia Complex mapping viewer by Kent Pearce (Texas Tech University), with links to other sites with applets using complex variables Other physics stuff Quantum scattering and tunnelling: pictures and animations generated by Chris Muktar (here in Manchester) as part of his second year computing project (pdf file, 1.9 MB); MATLAB program available from The Mathworks Cosmology by Max Tegmark (MIT) The cosmological microwave background by Wayne Hu (University of Chicago) Mathematicians and physicists To learn more about Fourier, Legendre, Bessel and the other mathematicians and mathematical physicists who contributed to the ideas we have been using, see their biographies on the St Andrews history of mathematics archive.

20th December 2007

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