MATH 257 Midterm: MATH 257+316 2016 Winter Test 1
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Be sure that this examination has 20 pages including this cover. 2 11 formula sheet has been provided. Notes are permitted only on the back of the formula sheet. The plea of accident or forgetfulness shall not be received: candidates must not destroy or mutilate any examination material; must hand in all examination papers; and must not take any examination material from the. 20 examination room without permission of the invigilator. [20] 1. (a) fourier series: compute the fourier sine series of f (x), de ned on [0, ] by f (x) = cos x. Page 3 of 20 pages (b) consider the following boundary value problem for laplace"s equation on half an annulus. urr + 1 r2 u = 0, u(r, 0) = 0, 1 < r < 2, u(1, ) = sin 3 , 0 < < . u(2, ) = cos ,
