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Unformatted text preview: ∂u ∂t ( x,t ) = ∂ 2 u ∂x 2 (0 < x < π, t > 0) u (0 ,t ) = u ( π,t ) = 0 ( t > 0) u ( x, 0) = ex (0 < x < π ) 5. Find the formal solution of the problem ∂ 2 u ∂x 2 ( x,y ) + ∂ 2 u ∂y 2 ( x,y ) = 0 (0 < x < π, < y < 1) u (0 ,y ) = u ( π,y ) = 0 (0 < y < 1) ∂u ∂y ( x, 0) = 0 , u ( x, 1) = f ( x ) (0 < x < π ) 6. Let A be a square matrix, and let p be the characteristic polynomial of A . (a) If q is a polynomial such that q ( A ) = 0, show that q ( λ ) = 0 for each eigenvalue λ of A . (b) Show that if A is diagonalizable then p ( A ) = 0....
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 Spring '08
 Chorin
 Math, Characteristic polynomial, A Closed Book

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