Differential Equations Lecture Work Solutions 40

Differential Equations Lecture Work Solutions 40 - 5 4 3 2...

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Unformatted text preview: 5 4 3 2 1 0 −1 −8 −L −6 −4 −2 −6 −4 −2 L 0 2 0 2 4 6 8 4 6 8 6 4 2 0 −8 −L L Figure 21: Sketch of f (x) and its periodic extension for 1c 6 4 2 0 −L L −2 −4 −6 −8 −6 −4 −2 0 2 4 6 8 4 6 8 6 4 2 0 −L L −2 −4 −6 −8 −6 −4 −2 0 2 Figure 22: Sketch of the odd extension and its periodic extension for 1c 1. c. The Fourier series is the same as the periodic extension. In fact the Fourier cosine series is the same!!! For the Fourier sine series we take ONLY the right branch on the interval [0, L] and extend it as an odd function. Now the same discontinuities are there but the value of the Fourier series at those points is 1 + (−1) =0 2 40 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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