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Differential Equations Lecture Work Solutions 37

Differential Equations Lecture Work Solutions 37 - 6 4 2 0...

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-8 -6 -4 -2 0 2 4 6 8 -6 -4 -2 0 2 4 6 -L L -8 -6 -4 -2 0 2 4 6 8 -6 -4 -2 0 2 4 6 -L L Figure 15: Sketch of f ( x ) and its periodic extension for 1a -8 -6 -4 -2 0 2 4 6 8 -6 -4 -2 0 2 4 6 -L L -8 -6 -4 -2 0 2 4 6 8 -6 -4 -2 0 2 4 6 -L L Figure 16: Sketch of the odd extension and its periodic extension for 1a 1. a. The Fourier series is the same as the periodic extension except for the points of discon- tinuities where the Fourier series yields 1 + 0 2 = 1 2 For the Fourier sine series we take ONLY the right branch on the interval [0
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