Differential Equations Lecture Work Solutions 44

Differential Equations Lecture Work Solutions 44 - 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 29: Sketch of f (x) and its periodic extension for problem 3 3. f (x) = 1 x < L/6 3 L/6 < x < L/2 0 x > L/2 Fourier cosine series coefficients: L/6 2 L L/2 0 L/6 0 an = 2 L = 2 L sin = 2 L sin = 2L L nπ cos nπ L nπ L nπ 6 nπ L 3 dx + nπ L x L/6 |0 +3 L/6 L/2 L/6 x dx + 3 +3 sin nπ 2 sin nπ L nπ L − sin nπ 6 2 L L +3 6 2 L 2L L +3 6 6 cos nπ L L L − 2 6 = 7 7 2 · L= L6 3 x dx x L/2 |L/6 nπ 6 nπ − 2 sin 2 for n even sin 0 3 dx = = a0 = nπ 6 ± 1 for n odd 44 = 2 nπ 3 sin nπ 2 − 2 sin nπ 6 ...
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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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