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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 + n =1 a n cos n π L x a 0 = 2 2 L L L/ 2 dx = 1 L L L 2 = 1 2 a n = 2 L L L/ 2 cos n π L x dx = 2 L L n π sin n π L x L L/ 2 = 2 n π sin n π 2 u ( x, t ) = 1 2 + n =1 2 n π sin n π 2 cos n π L x e k ( n π L ) 2 t b. f ( x ) = 6 + 4 cos 3 π L x = a 0 + n =1 a n
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