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Unformatted text preview: 18.03 Problem Set 8 Spring 2009 Due in Room 2-106 at 12:55 pm, Friday, April 17 Part A (14 points) 1. Lec 26, Fri April 10, Laplace Transform I, Basic properties. Read: EP 4.1; H (if you did not read it already) Work: 3A-2, 3cd, EP 4.1/ 5, 7, 8, 9. 2. Lec 27, Mon April 13, Laplace Transform II, Solving ODE Read: EP 4.2, 4.3 Work: 3A-9, 10ac; 3B-1ade, 3a, 5b; 3D-7 3. Lec 28, Wed April 15, Laplace Transform III: Convolution; weight functions Read: EP 4.4 Work: 3C-1b, 2b; 3D-4b Part B (34 points) 0. (at due date) Write the names of any person, web site, or materials you consulted. Write “No C” (no consultation) on your paper if you consulted no outside materials/people. 1. (Lec 26, Fri, April 10: Laplace Transform I) (5 pts: 1 + 1 + 2 + 1 ) a) Show directly from the definition of the Laplace transform that if F ( s ) = L ( f ( t )), then L ( e at f ( t )) = F ( s − a ). b) Find the Laplace transform of u ( t − a ) f ( t − a ) in terms of F ( s ) where a ≥ 0....
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This note was uploaded on 05/06/2010 for the course 18 18.03 taught by Professor Unknown during the Spring '09 term at MIT.
- Spring '09