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: Solutions for Homework 8, Math 20E, Winter 2009 Page 559 Problem 5 Let P ( x, y ) = f ( x ) and Q ( x, y ) = f ( y ). Then P y = y f ( x ) = 0 and Q x = x f ( y ) = 0, since f ( x ) does not depend on y and f ( y ) does not de pend on x . Thus by corollary 1 on page 557, there is a function g ( x, y ) such that F = g . Problem 6a Let r ( x, y, z ) = ( x, y, z ) and r ( x, y, z ) = ( x 2 + y 2 + z 2 ) 1 2 = k r ( x, y, z ) k . Then 1 r = ( x 2 + y 2 + z 2 ) 1 2 , so 1 r = ( 1 2 ( x 2 + y 2 + z 2 ) 3 2 (2 x ) , 1 2 ( x 2 + y 2 + z 2 ) 3 2 (2 y, 1 2 ( x 2 + y 2 + z 2 ) 3 2 (2 z )) = ( x r 3 , y r 3 , z r 3 ) = r k r k 3 . Problem 6b There are many ways to describe what it means to move a particle to . Here is one: Since F = 1 r , we know that the work done in moving a particle from r to another point q is independent of the path along which the particle travels (theorem 7 on page 551), and in fact for any curve ( t ) connecting them (oriented to start at r and end at q...
View
Full
Document
This note was uploaded on 01/30/2010 for the course MATH 20E 20E taught by Professor Enright during the Fall '09 term at UCSD.
 Fall '09
 Enright

Click to edit the document details