Here is the official site from the department.

Time and place: Monday 2-3 in B3.03 and Tuesday 5-7pm in A1.01. Supervisions Tuesday 4-5 in C1.06 (17 January) and L5 (other days) by Stephen Tate.

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.

We follow the book of Stein and Shakarchi (see the references below) with an extra chapter on distributions.

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

Assignments:
 Assignment 1: Exercises 2, 4, 6, 7, 8 on pages 59-61. Assignment 2: Exercises 12, 13, 14, 19 on pages 62-64. Assignment 3: Exercises 12, 13, 14, 15 on pages 91-92. Assignment 4: Exercises 11, 12, 13, 15, 23 on pages 164-169. Assignment 5: Exercises 4, 7, 8, and Problem 3, on pages 208-214. Assignment 6: Exercises 5, 6, 10 on pages 209-211. Assignment 7: All the exercises of the notes on distributions. Assignment 8: Exercises 3, 4, 5, 6, 13 on pages 236-239.

References:

The main reference is Fourier Analysis of E.M. Stein and R. Shakarchi, Princeton, 2003. The assignments above refer to this book. But the following references are very much worth studying:
• G. Frieseke, Lectures on Fourier Analysis, 2007.

• A. Pinkus and S. Zafrany, Fourier Series and Integral Transforms, Cambridge, 1997.

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

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

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

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