coming back to Math Academy to give guest lectures on Fourier series

This past Monday and Tuesday, I went back to Pasadena High School to give two lectures on Fourier series! The goal of my lectures was to prove Parseval’s theorem:

If $f$ is a continuous real-valued function with period $2\pi$, then $\sum_{n=0}^\infty c_n^2 = \int_{-\pi}^\pi [f(x)]^2 dx$, where $c_n$ are the Fourier coefficients of $f$ with respect to the orthonormal functions $\{\frac{1}{\sqrt{2\pi}}, \frac{\cos(x)}{\sqrt{\pi}}, \frac{\sin(x)}{\sqrt{\pi}}, \ldots\}$.

Then we used this to solve the Basel problem.

The notes from my lectures are available here. I also assigned homework, available here.