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)=a02+∑n=1[ancos(nx)+bnsin(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.