This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ACM 95/100c May 21, 2004 Problem Set VII 0. (2 pts) Write down your gradingsection 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 zaxis. In any ( x,y ) plane with y as a vertical coordinate the pipe can be modeled as a point source of heat, and the ground surface can...
View
Full
Document
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.
 Spring '09
 NilesA.Pierce

Click to edit the document details