Lecture
This lecture covers the solution of differential equations with periodic data, focusing on finding a periodic function that satisfies a given equation. The instructor explains the use of Fourier series to express the solution in terms of Fourier coefficients. The lecture then delves into the heat equation in R, a fundamental equation that describes temperature variations in a conducting bar. The instructor demonstrates the step-by-step process of solving the heat equation using Fourier transforms and inverse transforms, providing insights into the physical interpretations of the solutions. The lecture concludes by highlighting the importance of Fourier series in solving differential equations with periodic data and previews upcoming topics on partial differential equations.