The Fourier Series via Linear Algebra

I didn’t post last week because I was on vacation. But on vacation I decided to write about something a little out of my comfort zone: Fourier series. (Yeah. Try being my wife.)

Fourier series (and the related Fourier transform) made some sense to me for, but I never really learned how to derive them so they always seemed a bit magical. As I was going through Arthur Mattuck’s excellent differential equations course at MIT’s Open Courseware, the Fourier series clicked for me, so I thought I’d distill this out.

I’m tempted to categorize this post under “things Isaac should have learned in school (had he been paying attention), but I don’t think I ever had a course that taught this. If you’re still paying attention, I will assume that you recall your basic linear algebra and have some idea (and interest in) what a Fourier series is. But given that, this isn’t hard.

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