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Unformatted text preview: u t ( x,t ) = 2 u x 2 (0 < x < , t > 0) u (0 ,t ) = u ( ,t ) = 0 ( t > 0) u ( x, 0) = ex (0 < x < ) 5. Find the formal solution of the problem 2 u x 2 ( x,y ) + 2 u y 2 ( x,y ) = 0 (0 < x < , < y < 1) u (0 ,y ) = u ( ,y ) = 0 (0 < y < 1) u y ( x, 0) = 0 , u ( x, 1) = f ( x ) (0 < x < ) 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 ( ) = 0 for each eigenvalue of A . (b) Show that if A is diagonalizable then p ( A ) = 0....
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This note was uploaded on 01/12/2010 for the course MATH 54 taught by Professor Chorin during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Chorin
 Math

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