Lecture 8: Fourier Series for Functions with Arbitrary Period. Half-Range Expansions

This lecture covers Fourier series for functions with any period, not just 2. It explains how to adjust the formulas using a simple change of variable. The second half focuses on half-range expansions: when a function is only defined on half an interval, it can be extended as an even function to produce a cosine series or as an odd function to produce a sine series. Worked examples include rectangular and sawtooth waves. The lecture also discusses convergence at endpoints and connects the choice of series to physical problems, such as heat conduction in a rod with insulated or fixed-temperature ends. A summary of key formulas is provided, along with a preview of complex Fourier series.