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In mathematics, a Fourier
series decomposes a periodic function or periodic signal into a sum of simple oscillating functions, namely sines
and cosines (or complex exponentials). The study of Fourier series is a branch of Fourier analysis. Fourier series
were introduced by Joseph Fourier (1768–1830) for the purpose of solving the heat equation in a metal plate. It
led to a revolution in mathematics, forcing mathematicians to reexamine the foundations of mathematics and leading
to many modern theories such as Lebesgue integration.
Here are the Fourier Series for a few of the simplest and most common waveforms.