MATH 317 Midterm: MATH317 Fall 2008 Exam
31 Jan 2019
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Instructions: all questions carry equal weight, answer 6 or 7 questions; credit will be given for the best 6 answers, answer questions in the exam book provided. Start each answer on a new page: this is a closed book exam, notes and textbooks are not permitted, non-programmable calculators are permitted, translation dictionaries (english-french) are permitted. This exam comprises of the cover page, and 3 pages of 7 questions. 1. (a) state the fixed point theorem, which gives su cient conditions for an iteration xn+1 = g(xn) to converge to a xed point. (b) consider the iteration with g(x) = x + 1. Then divided di erences can be de ned recursively using the formula f [xi, xi+1, . , xi+j 1] xi+j xi (a) de ne the zeroth divided di erences f [xj] for j = 0, 1, . Xj=0 cjwj(x) be the newton form of the interpolating polynomial based on x0, x1, .
