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Unformatted text preview: MATH 3705A Test 3 Solutions March 16, 2007 Questions 1-2 are multiple choice. Circle the correct answer. Only the answer will be marked. [Marks] 1. At x = 59, the Fourier sine series of f ( x ) = 2 , x < 2 , 2 x 3 converges to  (a) -2 (b) -1 (c) 0 (d) 1 (e) None of these Solution: (a) 2. The solution of Laplaces equation u xx + u yy = 0 within the rectangle  < x < 2 , < y < 3, which satisfies the boundary conditions u (0 , y ) = 0 , u (2 , y ) = 0 , u ( x, 0) = x 2 , u ( x, 3) = 0 is: (a) u ( x, t ) = X n =1 a n sinh nx 3 sin ny 3 (b) u ( x, t ) = X n =1 a n sinh n (2- x ) 3 sin ny 3 (c) u ( x, t ) = X n =1 a n sinh n (3- y ) 2 sin nx 2 (d) u ( x, t ) = X n =1 a n sinh nx 2 sin ny 3 (e) None of the above Solution: (c) 3. The solution of the wave equation u xx = 1 c 2 u tt , < x < L , which satisfies the bound-  ary conditions u (0 , t ) = u ( L, t ) = 0, is given by u ( x, t ) = X n =1 sin nx L a n cos nct L + b n sin nct...
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This note was uploaded on 07/16/2009 for the course MATH 3705 taught by Professor Jaberabdualrahman during the Winter '08 term at Carleton CA.
- Winter '08