This was a course I lectured at Imperial in 2015/16. It's mainly fairly classical material about distribution theory and the Fourier transform. There's an appendix that covers some basic theory for topological vector spaces in order to justify assumptions about the topology of the space of test functions made elsewhere in the notes.

  • Introduction: a motivating example
  • Chapter 1: Test functions
  • Chapter 2: Distributions
  • Chapter 3: The Fourier transform
  • Chapter 4: Sobolev spaces and PDE
  • Appendix: Topological vector spaces

As with all the notes on my site, beware of errors!