MATH 316 Study Guide - Midterm Guide: Frobenius Method, Regular Singular Point
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Do not open this test until instructed to do so. It is a closed book exam; no textbooks, calculators, laptops, formula sheets or other aids are allowed. Turn o any cell phones, pagers, etc. that could make noise during the exam. You must remain in this room until you have nished the exam. Please explain your work, and circle your nal solutions. Consider the problem: uxx + uyy 2u = 0, u(x, 0) = 0, u(x, ) = 0, ux(0, y) = 0, ux( , y) = f (y). 0 < x, y < , t > 0, Find the general form of the solution u(x, y) and explain how series coe cients are to be determined in terms of f (y). 0 < x < 8, t > 0, ux(0, t) = 0, ux(8, t) = 0, u(x, 0) = f (x) =( 1.
