Differential Equations Lecture Work Solutions 42

Differential Equations Lecture Work Solutions 42 - 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 25: Sketch of the even extension and its periodic extension for 1d 4 3 2 1 0 −L L −1 −2 −3 −4 −8 −6 −4 −2 0 2 4 6 8 Figure 26: Sketch of the odd extension for 2 2. cos πx = L ∞ n=1 bn sin nπ x L bn = 0 n odd 4n π (n2 − 1) n even Since we have a Fourier sine series, we need the odd extension of f (x) Now extend by periodicity At points of discontinuity the Fourier series give zero. 42 ...
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