Sturm-Liouville Problem and Differential Equations

This lecture, recorded on April 20, 2020, covers the Sturm-Liouville problem, a key concept in the course. The instructor explains the nature of solutions to a specific differential equation and introduces the Sturm-Liouville problem, emphasizing the search for non-trivial solutions. The lecture delves into the analysis of different cases, such as lambda being zero, negative, or positive, and explores the conditions for non-trivial solutions. Additionally, the instructor discusses solving differential equations using Fourier transforms, focusing on finding solutions that satisfy specific conditions. The lecture concludes with a detailed explanation of the convolution product and its application to solving differential equations.