s7_95c - ACM 95/100c May 21, 2004 Problem Set VII 0.- (2...

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Unformatted text preview: ACM 95/100c May 21, 2004 Problem Set VII 0.- (2 pts) Write down your grading-section number. 1.- (20 pts) Consider the solution of Laplaces equation inside the interior of a circle 2 = 0 , , r < a, < 2 with Dirichlet boundary data ( a, ) = f ( ) (a) (5 pts) Show that the solution of this equation can be expressed in terms of the Greens function G ( x | ) defined by 2 G = ( x- ) , r < a, < 2 with G = 0 on r = a . (b) (10 pts) Using the method of images, write down the solution for G . (c) (5 pts) Show that the solution can be expressed in the form of the Poisson formula ( r, ) = 1 2 Z 2 f ( ) a 2- r 2 r 2 + a 2- 2 ar cos( - ) d [See Haberman, Edition 3, Section 8.5]. 2.- (25 pts) An effectively infinite horizontal pipe carrying a hot liquid is buried at a distance b below the horizontal ground surface, and lies parallel to the z-axis. In any ( x,y ) plane with y as a vertical co-ordinate the pipe can be modeled as a point source of heat, and the ground surface can...
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This note was uploaded on 01/08/2011 for the course ACM 95c taught by Professor Nilesa.pierce during the Spring '09 term at Caltech.

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s7_95c - ACM 95/100c May 21, 2004 Problem Set VII 0.- (2...

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