I am teaching the second half of this unit (approximately weeks 18-23). Please check the official online unit description. For the first half of the unit, and some other resources such as maple animations, please see Diki Porter's page. Past exams are on Bb, in the "organisation" Maths Teaching.
Revision Timetable:
Maths cafe sessions (Thursdays and alternate Fridays at 4:10):
While not directly intended for this unit, you may find some of my old material for Methods 3 and (the discontinued) Applied Mathematics 2 helpful.
Some relevant research (well beyond the scope of this course):If a box is equally split into two regions in which a particle can diffuse at different rates, what fraction of time does it spend in each region? This apparently simple question has a rather subtle answer and is the subject of a recent preprint (ie paper that has not yet been published in a peer-reviewed journal) by Tupper and Yang.
The methods we used to study the modes of vibration of a drum can be applied to circular microdisks, which are used to construct lasers of a few microns in size. Under some approximations, the electromagnetic equations reduce to eigenvalues problems for the 2D Laplacian, matched at the boundary by conditions related to the refractive index of the material and the type of mode (transverse magnetic or electric). The solution inside is given in terms of J Bessel functions as the solution must be regular at the centre. The solution outside is given by Hankel functions, which are linear combinations of J and Y Bessel functions appropriate for outgoing waves at infinity. See this paper which was published in EPL 87 34003 (2009).