Assorted Flavors of Fourier Series on a Finite Domain

Choose the one that behaves nicely at the boundaries

If you look up the history of Fourier analysis, you’ll see that Jean-Baptiste Joseph Fourier formalized the series that would bear his name while working on the heat flow problem.

A Fourier series represents a periodic signal as a sum of sinusoids whose frequencies are integer multiple of the fundamental frequency.

We intuitively know that a hot spot in a conductive medium will spread heat …

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