# 4.2: Introduction to Fourier Series

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Rather than Taylor series, that are supposed to work for “any” function, we shall study periodic functions. For periodic functions the French mathematician introduced a series in terms of sines and cosines,

\[f(x) = \frac{a_0}{2} + \sum_{n=1} [a_n\cos(nx)+b_n\sin(nx)].\]

We shall study how and when a function can be described by a Fourier series. One of the very important diﬀerences with Taylor series is that they can be used to approximate non-continuous functions as well as continuous ones.