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wksht07

# wksht07 - MATH 152 L1 L2 Applied Linear Algebra and...

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MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 07 Worksheet (March 14, 2005) : Laplace Transform Q1. (Inverse Laplace transform) Find the inverse Laplace transform of F ( s ) = e - π 3 s s 2 + 1 . [ Hint . You may use the formula L - 1 { e - as G ( s ) } = u 0 ( t - a ) g ( t - a ), where G ( s ) = L{ g ( t ) } .] Q2. (Impulse function) Use Laplace transform to solve the boundary value problem (BVP) y 00 + y = 2 δ ( t - π 3 ) , 0 6 t 6 π 2 , y (0) = 0 , y ( π 2 ) = 1 2 . [ Hint . You may first assume that y 0 (0) = A . Then use the Laplace method to solve the initial value

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