Here is the official site from the department.

Time and place: Monday 1-2 in MS.03, Thursday 12-1 in B3.03, and Friday 10-11 in B3.02. Support classes Friday 12-1 in P5.21 by Dom Kerr.

Assessment: 3-hour examination.

Description:
Fourier series and Fourier transform have numerous applications in PDEs, functional analysis, probability theory, and even number theory! We will study their definitions and properties, and consider specific applications.

I occasionally put comments on my facebook page; but anything of importance can also be found here.

Assignments:
Assignment 1
Assignment 2
Assignment 3
Assignment 4
Assignment 5
Assignment 6
Assignment 7
Assignment 8


Handwritten notes:
Notes, pages 1-8
Notes, pages 9-16
Notes, pages 17-24
Notes, pages 25-32
Notes, pages 33-40
Notes, pages 41-48
Notes, pages 49-56
Notes, pages 57-64
Notes, pages 65-72
Notes, pages 73-80
Notes, pages 81-87

References:

  • J. Duoandikoetxea, Fourier Analysis, AMS, 2001.

  • G.B. Folland, Real Analysis, Wiley, 1999.

  • G. Frieseke, Lectures on Fourier Analysis, 2007.

  • J.K. Hunter and B. Nachtergaele, Applied Analysis, World Scientific, 2001. (This book is available online.)

  • E.H. Lieb and M. Loss, Analysis, AMS, 2001.

  • M. Reed and B. Simon, Fourier Analysis, Self-Adjointness (Methods of Modern Mathematical Physics II), Elsevier, 1975.

  • E.M. Stein and R. Shakarchi, Fourier Analysis, Princeton, 2003.