Fourier Transform: Definition and Properties

This lecture introduces the concept of Fourier transform, explaining how it is related to Fourier series and how it can be used to approximate non-periodic functions using complex exponentials. The instructor covers the definition of the Fourier transform, its inverse, and the reciprocity theorem. Through examples and mathematical derivations, the lecture demonstrates how the Fourier transform can be applied to continuous functions and how the inverse transform can recover the original function. The properties of the Fourier transform are discussed, emphasizing its utility in solving differential equations in a more efficient way compared to traditional methods. The lecture concludes with a practical demonstration of applying the Fourier transform to a specific real function.