Fourier Analysis and PDEs

This lecture covers the historical context of Fourier analysis and partial differential equations, focusing on the 19th century. It discusses the correspondence between D. Bernoulli and L. Euler in 1753, as well as Newton's law of cooling. The lecture then delves into the heat equation on a metal plate in R², exploring the concept of heat flow and temperature distribution. The presentation continues with the Laplace equation in polar coordinates, emphasizing the Dirichlet problem and the solution through separation of variables. The lecture concludes with the discussion of periodic boundary conditions and the Laplacian operator, showcasing the process of finding solutions through linear combinations.