Fourier Transformation: Solving Differential Equations

This lecture delves into the Fourier transformation as a tool to solve differential equations, focusing on the Poisson problem on the real line. The instructor explains the process of transforming the differential equation, isolating the Fourier transform, and applying the inverse Fourier transform. Through a specific example, the lecture demonstrates the convolution operator and the computation involved. The solution formula is derived step by step, considering different cases and making necessary distinctions. The lecture concludes by discussing the symmetry property of the solution and its relation to the initial source term.