Differential Equations Lecture Work Solutions 46

Differential Equations Lecture Work Solutions 46 - 2 1 0...

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Unformatted text preview: 2 1 0 −1 −2 −10 −5 0 5 10 −10 −5 0 5 10 2 1 0 −1 −2 Figure 31: Sketch of the periodic extension of the odd extension of f (x) (problem 5) 5. f (x) = 1 0 < x < π/2 0 π/2 < x < π Expand in series of sin nx f (x) ∼ π n=1 bn = 2 π π 0 bn sin nx f (x) sin nx dx = 2 π π /2 0 1 · sin nx dx ↑ f (x) = zero on the rest = 2 π =− − 1 cos nx n π/2 |0 nπ 2 2 cos + nπ 2 nπ ↑ this takes the values 0, ± 1 depending on n !!! 46 ...
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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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