Differential Equations Lecture Work Solutions 29

Differential Equations Lecture Work Solutions 29 - 7 6 5 4...

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Unformatted text preview: 7 6 5 4 3 2 1 0 −1 −10 −L −8 −6 −4 −2 L 0 2 4 6 8 10 Figure 6: Graph of f (x) = ex 7 6 5 4 3 2 1 0 −1 −10 −4L −8 −3L −6 −2L −4 −L −2 L 0 2L 3L 4L 2 4 6 8 10 Figure 7: Graph of its periodic extension 1. c. f (x) = ex Since the periodic extension of f (x) is discontinuous, the Fourier series is identical to (the periodic extension of) f (x) everywhere except for the points of discontinuities. At x = ±L (and similar points in each period), we have the average value, i.e. eL + e−L = cosh L 2 29 ...
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