Solving Poisson Problem: Fourier Transform Approach

This lecture covers the application of the Fourier transform to solve the Poisson problem in both bounded and unbounded domains. The instructor explains the concept of convolution, linearity, and commutativity of the convolution operation, highlighting its importance in transforming convolutions into multiplications in the Fourier domain. By leveraging the properties of the Fourier transform, the instructor demonstrates how to express the solution to the Poisson problem in terms of the inverse Fourier transform of the convolution of the given function with the Fourier transform of the problem data. The lecture concludes with a detailed explanation of how to use the Fourier transform to simplify the solution process and obtain an explicit expression for the solution.