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Mathematics LibreTexts

4.2: Introduction to Fourier Series

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    8356
    • [ "article:topic", "authorname:nwalet", "license:ccbyncsa" ]

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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.