Differential Equations Lecture Work Solutions 38

Differential Equations Lecture Work Solutions 38 - 6 4 2 0...

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Unformatted text preview: 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 17: Sketch of the even extension and its periodic extension for 1a 6 4 2 0 −8 −L −6 −4 −2 −6 −4 −2 L 0 2 0 4 2 6 8 4 6 8 6 4 2 0 −8 −L L Figure 18: Sketch of f (x) and its periodic extension for 1b 1. b. The Fourier series is the same as the periodic extension except for the points of discontinuities where the Fourier series yields eL + e−L = cosh L 2 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 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 19: Sketch of the odd extension and its periodic extension for 1b 38 ...
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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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