Numerical Methods: Boundary Value Problems

This lecture covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and using it to solve partial differential equations (PDEs) through spectral methods. It introduces Finite Element Methods and explains the Crank-Nicolson method. The lecture also explores de-noising data using FFT, image processing with 2D FFT, and solving PDEs with spectral methods like the heat equation. It delves into the Galerkin approximation in Finite Element Methods, discussing the advantages of FEM and software packages for implementation. The lecture concludes with practical exercises on the one-way wave equation and calculating the column vector F for the finite element method solution.