Differential Equations Lecture Work Solutions 31

Differential Equations Lecture Work Solutions 31 - 8 6 4 2...

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Unformatted text preview: 8 6 4 2 0 −L L −2 −4 −10 −8 −6 −4 −2 0 2 4 6 8 10 Figure 10: Graph of f (x) 8 6 4 2 0 −4L −3L −2L −L L 2L 3L 4L 2 4 6 8 −2 −4 −10 −8 −6 −4 −2 0 10 Figure 11: Graph of its periodic extension 1. e. Since the periodic extension of f (x) is discontinuous, the Fourier series is identical to (the periodic extension of) f (x) everywhere except at the points of discontinuities. At those points x = ±L (and similar points in each period), we have 1 L2 + 0 = L2 2 2 At the point L/2 and similar ones in each period we have 0 + 1 L2 1 4 = L2 2 8 31 ...
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