## Fourier series notes

When the French mathematician Joseph Fourier (1768–1830) was trying to solve a problem
in heat conduction, he needed to express a function as an infinite series of sine and
cosine function:

Earlier, Daniel Bernoulli and Leonard Euler had used such series while investigating problems
concerning vibrating strings and astronomy.
The series in Equation 1 is called a trigonometric series or Fourier series and it turns
out that expressing a function as a Fourier series is sometimes more advantageous than
expanding it as a power series. In particular, astronomical phenomena are usually periodic,
as are heartbeats, tides, and vibrating strings, so it makes sense to express them in terms
of periodic functions.

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