f_spring10

f_spring10 - Final Exam Math 2930 show work 13 questions on...

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Final Exam Math 2930 Spring 2010 show work, 13 questions on 7 pages, no calculators some answers will fit into a box; box your answers wherever possible 1) (4 points) Write your name and section number at the top of this page. 2) (6 points) Consider the period 2 π function f given by f ( x ) = e bx when - π x < π . Here b is a positive constant. Sketch the graph of f for 3 full periods. To what does the Fourier series of f converge, at the points x = π and at x = 0? Find (only) the constant a 0 2 term of the series. 3) (10 points) Newton wants to build a house in an environment where the temperature goes through one cycle each year, and he thinks the inside temperature T ( t ) of the house will vary according to T = - 1 10 ( T - 20 cos( at ) ) . But he doesn’t know what to use for a . If t is in days, figure out a reasonable choice for the value of a . Then solve Newton’s equation. T ( t ) = a = 1

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4) (10 points) Solve for y ( x ) 0 = ky ( x ) + C with boundary conditions y (0) = 0, y ( L ) = 0. Here k , C and L are given, unspecified positive constants.
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