worksheet - Worksheet - November 6, 2008 (1) Consider the...

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Unformatted text preview: Worksheet - November 6, 2008 (1) Consider the eigenvalue problem y +y = 0 ; (a) Find all the eigenvalues > 0. y(0) = y(1) = 0 (1) (2) Consider the following differential equation y + xy = 0 (a) Assume a power series solution and find the recurrence relation. (b) Find the radius of convergence. (c) Find the power series solution of eq.(2). (2) (3) Consider the following 2 periodic function f(t) = t2 , (a) Find its Fourier series. - t< (3) Hints and Partial Answers (1a) n = n2 2 cn (2a) cn+3 = - (n+2)(n+3) (2b) = (2c) y(x) = c0 1 + n=1 (-1)n x3n (-1)n x3n+1 + c1 n n! 2 5 (3n - 1) n n! 1 4 (3n + 1) 3 3 n=0 2 cos t cos 2t cos 3t cos 4t (3a) f(t) -4 - + - + 3 1 22 32 42 584 19 ...
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This note was uploaded on 11/09/2008 for the course MATH 2930 taught by Professor Terrell,r during the Fall '07 term at Cornell University (Engineering School).

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worksheet - Worksheet - November 6, 2008 (1) Consider the...

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