In this talk, we introduce the Fourier series of integrable functions and discuss some convergence issues. It is well known that Fourier series of all integrable functions need not converge. In this lecture, we show that for sufficiently smooth functions, the Fourier series indeed converges to the function uniformly. We also discuss other notions of convergence of Fourier series.
Note: This lecture will be elementary and intended for BSMS students.