Differential Equations Lecture Work Solutions 53

Differential Equations Lecture Work Solutions 53 - 2. ut =...

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2. u t = ku xx u x (0 ,t )=0 u x ( L, t u ( x, 0) = f ( x ) u ( x, t )= X ( x ) T ( t ) ˙ Tx = kX 0 T ˙ T kT = X 0 x = λ ˙ T + λkT =0 X 0 + λX X 0 (0) = 0 X 0 ( L X n = A n cos nπx L ,n =1 , 2 ,... λ n = L ± 2 , 2 λ 0 X 0 = A 0 ˙ T n + L ± 2 n T n = B n e ( L ) 2 kt u ( x, t A 0 B 0 | {z } = a 0 + X n =1 A n cos L B n e ( L ) 2 u ( x, t
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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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