Differential Equations Lecture Work Solutions 54

Differential Equations Lecture Work Solutions 54 - a. f (x)...

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a. f ( x )= 0 x<L / 2 1 x>L / 2 u ( x, 0) = f ( x )= a 0 + X n =1 a n cos L x a 0 = 2 2 L Z L L/ 2 dx = 1 L L L 2 ± = 1 2 a n = 2 L Z L L/ 2 cos L xdx = 2 L L sin L x L L/ 2 = 2 sin 2 u ( x, t )= 1 2 + X n =1 2 sin 2 ± cos L xe k ( L ) 2 t b. f ( x )=6+4co s 3 π L x = a 0 + X
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