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4.2: Introduction to Fourier Series

Last updated

Jul 4, 2022
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- 4.1: Taylor Series
- 4.3: Periodic Functions

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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,

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

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.

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