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Unformatted text preview: AMATH 351 Problem Set No. 8 Fall 2005 Reminder: Final examination on Tuesday, December 20, 2005, 12:30 - 15:00 in RCH 306. Nonpro- grammable calculators allowed. No other aids allowed. Formula sheets will be provided with the exam. Version 1.0 dated 1 December 2005 - an updated version will be posted on the library website by December 7, 2005 Laplace Transforms, Convolutions, Dirac Delta Functions 1. Suggested problems from Problem Set No. 5, AM 351 Course Notes: 5-9, 14-17. 2. Solve the following integral equations using Laplace transforms: (a) y ( x ) = 1- integraldisplay x ( x- t ) y ( t ) dt, (b) e x = y ( x ) + 2 integraldisplay x cos( x- t ) y ( t ) dt. 3. Evaluate each of the following integrals involving the Dirac delta function: (a) integraldisplay 1 t 3 ( t- 1 3 ) dt. (b) integraldisplay 1 t 3 ( t + 1 3 ) dt. 4. Evaluate the following Laplace transforms involving the delta function: (a) L [ e t ( t- 2)] . (b) L [ e 3 t ( t- )] ....
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