MMfE - Examples of Fourier Series

All Exercises (with Solutions) containing the ""Fourier_series” or Fourier_series_convergence_type” tag:

• MMfE ~ exam_2020_06_10 - with solutions
• MMfE ~ exam_2021_02_17 - with solutions

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General Solution

MMfE - Fourier Series

• Online Resources: mathisfun

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Def.: Fourier Series

Given a function $f(x)$ we can rewrite it as:

$$f(x)=a_0+\sum _{n=1}^{\infty }{a}_n\cdot \cos (nx\frac{\pi }{L})+\sum _{n=1}^{\infty }{b}_n\cdot \sin (nx\frac{\pi }{L})$$

Where:

$$\begin{array}{rl}{a}_0& =\frac{1}{2L}{\int }_{-L}^{+L}f(x)dx\\ a_n& =\frac{1}{L}{\int }_{-L}^{+L}f(x)\cos (nx\frac{\pi }{L})dx\\ b_n& =\frac{1}{L}{\int }_{-L}^{+L}f(x)\sin (nx\frac{\pi }{L})dx\end{array}$$

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Link to original

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~Ex.: 2020_06_10 Point 2.

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Link to original

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Transclude of MMfE-~-exam_2021_02_17---with-solutions#ex-2021_02_17-point-2