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Unformatted text preview: u t = 2 u x 2 , < x < , t > BC : u (0 ,t ) = 0 = u ( ,t ) IC : u ( x, 0) = f ( x ) (a) Apply the method of separation of variables, and nd the solution if f ( x ) = 3 sin(2 x )sin(4 x ). [15 marks] (b) Find the Fourier series of the 2 periodic function f ( x ) with f ( x ) = 3 x on x . [5 marks] ( Hint: R  x sin( nx ) dx = 2 n (1) n +1 n = 1 , 2 , 3 ,.... ) (c) Use your answer to (b) to nd the solution of the above heat equation problem with f ( x ) = 3 x . [5 marks] 2...
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This note was uploaded on 04/06/2012 for the course MATH 257 taught by Professor Peirce during the Fall '08 term at The University of British Columbia.
 Fall '08
 PEIRCE
 Math

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