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Unformatted text preview: x = 0. Page 5 Name: Exercise 5. Determine wether the following series converge (Justify your answer): 1) ∞ X k =1 (1) k 2 k + 1 2) ∞ X k =1 e k e 2 k1 3) ∞ X k =1 1 2 k 21 Page 6 Name: Exercise 6. Find the solution for the wave equation: u tt25 u xx = 0 u (0 , t ) = 0 t ≥ u ( π, t ) = 0 t ≥ u ( x, 0) = 2 sin( x ) ≤ x ≤ π u t ( x, 0) = 3 sin(2 x ) ≤ x ≤ π u ( x, t ) = Page 7 Name: Exercise 7. Determine for which x the following series converges: ∞ X k =1 e kx Compute its value for all the values of x , for which it converges. Page 8 Name: Exercise 8. ( Extra) Let S be the surface deﬁned by z = x 2 + y 2 , z =x 2y 2 and x 2 + y 2 = 1 and let F = ( x + y, y + z, x 2 + z ). Compute Z Z S F n dσ = Page 9 Name: Page 10...
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 Fall '06
 Roche
 Math, Fourier Series, #, Partial differential equation, 1 1 2k

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