MATH 401 Study Guide - Midterm Guide: Weak Formulation, Eigenfunction, Dot Product

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9 Jan 2019
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Be sure that this examination has 4 pages including this cover. If more than 8 questions are attempted, the best 8 marks will be taken. Rules governing examinations: each candidate should be prepared to produce his or her library/ams card upon request, read and observe the following rules: No candidate shall be permitted to enter the examination room after the expiration of one half hour, or to leave during the rst half hour of the examination. Candidates are not permitted to ask questions of the invigilators, except in cases of supposed errors or ambiguities in examination questions. The plea of accident or forgetfulness shall not be received: smoking is not permitted during examinations. Consider the ode bvp for u(x), x [0, 1] given below: u + xu u = f (x), u(0) = 0, u(1) = 0. (a) [5 marks] find the adjoint of this problem. (b)