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Unformatted text preview: x = 0 to determine two independent solutions to (1). You only need to determine the f rst three non-zero terms in each case. [35 marks] 2. Apply the method of separation of variables to determine the solution to the one dimensional heat equation with the following homogeneous Dirichlet boundary conditions: u t = 2 u x 2 , < x < , t > BC : u (0 , t ) = 0 = u ( , t ) IC : u ( x, 0) = x ( x ) Hint: It may be useful to know that R x ( x ) sin( nx ) dx = 2 n 3 (1 cos( n )) . [30 marks] 1...
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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