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Differential Equations Lecture Work Solutions 41

Differential Equations Lecture Work Solutions 41 - 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 23: Sketch of f ( x ) and its periodic extension for 1d -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 24: Sketch of the odd extension and its periodic extension for 1d 1. d. 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 x = 0 + multiples of 4 1 + 2 2 = 3 2 for x = 2 + multiples of 4 For the Fourier sine series we take ONLY the right branch on the interval [0
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