Fourier Transform and Differential Equations

This lecture covers the Fourier transform and its applications in solving differential equations. The instructor begins with an overview of the evaluation methods for the course, including the structure of the exam and the types of questions that will be asked. The focus then shifts to the wave equation and its transformation using Fourier methods. The instructor explains the derivation of the wave equation and discusses the significance of the parameters involved. The lecture includes detailed examples of how to apply the Fourier transform to solve differential equations, emphasizing the relationship between the original function and its transformed counterpart. The instructor also addresses common pitfalls and clarifies the conditions under which the Fourier transform can be applied. Throughout the lecture, the importance of understanding the underlying mathematical principles is highlighted, ensuring that students grasp both the theoretical and practical aspects of the Fourier transform in the context of differential equations.