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Numerical Methods: Boundary Value Problems
This lecture covers the motivation behind boundary value problems, including examples like vertical deflection of a string and diffusion in a catalyst particle. It also explains the finite difference method in 1D, focusing on Joule heating in a wire. The instructor discusses the general description of boundary value problems and the strategies for employing the finite difference method to solve them. An example of Joule heating with Dirichlet boundary conditions is presented, demonstrating the application of numerical methods to find the temperature distribution in a metal wire.