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Unformatted text preview: ACM 95/100c Problem Set 8 22nd May 2006 Due by 5:00PM on 6/2/2006 Please deposit all problem sets in the slot in 303 Firestone Please remember to include your section number and section instructor Each problem is worth 10 points - each part of a multi-part problem is weighted equally Some of the solutions to some of the problems may be available from old solution sets. Your educational experience will be enhanced if you don't succumb to the temptation to use them but in general you can consult any written source out there for the non collaboration problems and you can collaborate freely on those problems marked collaboration allowed . This is the last problem set for the term. At the end of the problem set is a feedback form for the course and also for the streaming lectures. Please ll out the evaluation form and send it in to the EAS division o ce. The evaluation form for the streaming lectures goes to the Digital Media Center. Thanks, have a great summer vacation and congratulations to all graduates. Problem 1 (No collaboration) Consider the solution of Poisson's equation inside a circle of radius a : 2 u = f. with boundary conditions u ( a, ) = h 1 ( ) for 0 < < u r ( a, ) = h 2 ( ) for- < < Represent the solution u ( r, ) in terms of the Green's function which you can assume to be known but indicate what equation is satis ed by the Green's function and the boundary conditions for the Green's function as well. 1 Problem 2 (No collaboration) Determine the Green's function G ( x , x ) inside a sphere of radius a for Poisson's equation with Dirichlet boundary conditions given on the surface of the sphere....
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