Fourier Transform: Concepts and Applications

This lecture introduces the Fourier transform, a mathematical tool that extends the Fourier series to a broader class of functions. The instructor explains the formula for the Fourier transform, discusses different conventions in defining it, and emphasizes its applications in signal processing and differential equations. Through examples, the lecture demonstrates how to compute the Fourier transform and its inverse, highlighting properties like linearity and modulation. The Dirichlet theorem for the Fourier transform is presented, along with the concept of energy preservation. The lecture concludes by discussing the derivative property of the Fourier transform and its significance in solving differential equations.