Math 220 Extra Credit 10 Spring 2015 Date due: Monday, April 27, 2015 Put all work on separate paper. Collaboration is encouraged, but identical solutions will receive only one point. To receive full credit, you must provide complete solutions and not isolated answers with no justication. Late homework will not be graded. Extra credit work is optional and not required. (1) Compute the Fourier series for the function f (x) = e2x on the interval < x < . Use the table in the front of the book to evaluate the integrals. (2) Compute the Fourier series for the function f (x) = x2 on the interval < x < . Use the table in the front of the book to evaluate the integrals. Use your answer to evaluate the innite series 1 n2 n=1 (3) Compute the Fourier sine series of the function f (x) = cos x on the interval 0 < x < . Use the table in the front of the book to evaluate the integrals. (4) Use the general solution to solve the heat ow problem (1) (2) (3) 2u u (x, t) = 5 2 (x, t), 0 < x < , t > 0. t x u(0, t) = 0, u(, t) = 0, t > 0. u(x, 0) = cos x, 0 < x < . (5) Use the general solution to solve the heat ow problem (4) (5) (6) u 2u (x, t) = 4 2 (x, t), 0 < x < , t > 0. t x u(0, t) = 0, u(, t) = 0, t > 0. u(x, 0) = 1, 0 < x < . 1