= Solving partial differential equations with the Fourier series
See: https://math.stackexchange.com/questions/579453/real-world-application-of-fourier-series/3729366\#3729366 from <heat equation solution with Fourier series>.
<Separation of variables> of certain equations like the <heat equation> and <wave equation> are solved immediately by calculating the <Fourier series> of initial conditions!
Other basis besides the Fourier series show up for other equations, e.g.:
* <bessel function>
* <Hermite polynomials>