Fourier Series: Approximation and Convergence

This lecture covers the concept of Fourier series, which approximate periodic functions as infinite sums of sines and cosines. It explains the motivation behind Fourier series, the conditions for their existence, and their convergence properties. The lecture also introduces the Fourier coefficients and discusses the heuristic justification of the series definition. Additionally, it presents the Dirichlet theorem and explores the relationship between the Fourier series and the original function. The lecture concludes with examples of computing Fourier series and comparing them with the original functions.