Heat Equation in 1D: Chapter 12

This lecture covers the heat equation in 1D, focusing on the problem of heat transfer in a one-dimensional material. The instructor discusses the initial and boundary conditions, the material properties, and the temperature distribution over time. Various numerical methods, such as finite difference schemes, are introduced to approximate the solution. The lecture emphasizes the conservation of thermal energy and the principles of heat transfer. Different discretization techniques in time and space are explored to solve the differential equations efficiently.