Finite Difference Method: Approximating Derivatives and Equations

This lecture covers the finite difference method for approximating derivatives and solving differential equations. Starting with the basics of approximating second derivatives, the instructor explains how to apply this method to continuum problems. The lecture then delves into center difference equations of the fourth order for finer approximations. The general strategy for employing the finite difference method to solve one-dimensional boundary value problems is discussed, along with practical examples of joule heating with Dirichlet boundary conditions. The lecture concludes with a demonstration of discretizing the domain and applying finite difference approximations to solve differential equations.