Unbounded and Bounded Systems: Fourier Methods

This lecture covers the spectral properties of unbounded and bounded systems in the context of Fourier methods. It discusses the impact of boundary conditions on partial differential equation solutions, the extension of functions, and the representation of periodic and non-periodic functions using Fourier series. The instructor explains the importance of choosing the correct representation for different boundary conditions and provides insights into the complex exponential Fourier series. Various examples are used to illustrate the concepts, including the effect of boundary conditions on the solutions of partial differential equations.