set3_problems

# set3_problems - Sample for the Midterm 2 for MA527 1. Find...

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Sample for the Midterm 2 for MA527 1. Find the inverse Laplace transform of s 2 +6 ( s - 2)( s 2 +2 s +2) . 2. Find the inverse Laplace transform of e - 3 s s 2 +4 s +5 . 3. Compute u ( t - 1) * ( e - 2 t u ( t )) and its Laplace transform. 4. Solve y ( t ) = 2 t - 4 R t 0 y ( τ )( t - τ )d τ . 5. Solve y 00 + 2 y 0 - 3 y = 8 e - t + δ ( t - 1 / 2) y (0) = 3 y 0 (0) = - 5. 6. Find the Laplace transform of the π -periodic extension of the function f ( x ) = x deﬁned on the interval [0 , π ]. 7. Find all eigenfunctions and eigenvalues of the following boundary problem: y 00 + 2 y 0 + 2 y = 0 , y (0) = y ( π ) = 0 . 8. Find sine, cosine and complex Fourier transforms of the function f ( x ) = ± 0 , x < 0 xe - x , 0 x Find also the Laplace transform of f . Try not to repeat calculations. 9. Let f ( x ) = x be deﬁned on the interval [0 , π ]. (1) Find the Fourier series of its
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## This note was uploaded on 04/03/2012 for the course MA 527 taught by Professor Weitsman during the Spring '08 term at Purdue.

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