Differential Equations Lecture Work Solutions 34

Differential Equations Lecture Work Solutions 34 - 2. b....

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2. b. This function is already in a Fourier sine series form and thus we can read the coefficients a n =0 n =0 , 1 , 2 ,... b n =0 n 6 =1 b 1 =1 2. c. -6 -4 -2 0 2 4 6 -4 -2 0 2 4 6 8 -L L -L/2 L/2 Figure 14: graph of f ( x ) for problem 2c Since the function is even, all the coefficients b n will vanish. a 0 = 1 L Z L/ 2 L/ 2 dx = 1 L x | L/ 2 L/ 2 = 1 L ( L 2 ( L 2 )) = 1 a n = 1 L Z L/ 2 L/ 2 cos L xdx = 1 L L
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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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