The course PHYS 20171, Mathematics of Waves and Fields, is a prerequisite for this course. If you feel rusty, have a look at my website for the material for the related 2C1 course (walet.phy.umist.ac.uk/2C1)), which may help to refresh your memory.
In addition, the Section on Green Functions requires a simple knowledge of contour integration and the . The latter material has been covered in MATH 20612.
Alternatively, a student who has not attended this course should read Appendix A (about 10 pages) and the first two or three pages of section 3.3 of Matthews and Walker, Mathematical Methods of Physics. (The later pages of section 3.3 involve integrating around cuts and branch points, which will not be required here.) There is also a mathematica notebook (Contour.nb) available on the course web site walet.phy.umist.ac.uk/MaMe, as well as a pdf file (Contour.pdf), and much of the material is also summarised in Appendix A.