By J M F Tsang (j.m.f.tsang@cantab.net).
The quickest way to use these is with Binder: https://mybinder.org/v2/gh/jftsang/ibmethods-demos/master. But note that Binder environments expire after a few minutes of inactivity.
These demos are maintained on
GitHub at
jftsang/ibmethods-demos, and I welcome any contributions or
corrections.
Richard Jozsa's lecture notes from 2013 are probably the best reference for the material in this course (but check the Schedules). They can be found (together with many other resources for other courses) at http://www.damtp.cam.ac.uk/user/examples/.
The classic textbook for this course is Mathematical Methods for Physics and Engineering by Riley, Hobson and Bence, available at many libraries. It also covers large parts of Variational Principles and Complex Methods, amongst others (as well as the applied courses in Part IA).
The Handbook of Mathematical Functions by Abramowitz and Stegun is a good reference for formulae for special functions (such as Bessel functions). A scanned version is available online (big PDFs, be warned). The NIST Digital Library of Mathematical Functions is the successor of this book.
A YouTube series on distribution theory (might provide some insights about how to think about delta functions): https://www.youtube.com/watch?v=gwVEEUg8PBY
For those interested in rigorous foundations of the material in this course, An Introduction to Hilbert Space by Young (available online to Cambridge University members) and Partial Differential Equations by Evans (libraries) may be of interest. But be warned that the language and approach is very different from the one taken in this course.
These demos are licenced under Creative Commons Attribution-ShareAlike
4.0 International
Licence](http://creativecommons.org/licenses/by-sa/4.0). 
Please report any bugs, mistakes or suggestions to me, either by email
(j.m.f.tsang@cantab.net) or (preferably) on the Issues tab on GitHub.