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4.2: Introduction to Fourier Series

  • Page ID
    8356
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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.


    This page titled 4.2: Introduction to Fourier Series is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Niels Walet via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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