wksht07 - MATH 152 L1 & L2 Applied Linear Algebra...

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Unformatted text preview: MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Week 07 Worksheet (March 14, 2005): Laplace Transform Spring 2004-05 Q1. (Inverse Laplace transform) Find the inverse Laplace transform of [Hint. F (s) = e− 3 s . s2 + 1 π You may use the formula L−1 {e−as G(s)} = u0 (t − a) g (t − a), where G(s) = L{g (t)}.] Q2. (Impulse function) Use Laplace transform to solve the boundary value problem (BVP) π π y + y = 2 δ (t − ), 0 t , 3 2 y (0) = 0, π 1 y( ) = . 2 2 [Hint. You may first assume that y (0) = A. Then use the Laplace method to solve the initial value problem. Finally you can determine the constant A by making use of the boundary condition.] Q3. (Convolution integral) Use convolution integral to find the Laplace transform of t f (t) = 0 sin(t − τ ) cos τ dτ. Q4. (Convolution integral) Solve the initial value problem 4y + y = g (t), y (0) = 3, y (0) = −7. ...
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wksht07 - MATH 152 L1 & L2 Applied Linear Algebra...

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