assignment6

# assignment6 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

This preview shows pages 1–2. Sign up to view the full content.

THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 First Semester: Assignment 6 Due date: 2010 December 3 (Friday), 5:00pm. 1. Let F = M ( x,y ) i + N ( x,y ) j . The divergence theorem shows that the ﬂux of F across a closed curve C (i.e., H C F · n ds ) is equal to RR D ( M x + N y ) dA , where D is the region bounded by C . Use Green’s theorem to establish a similar result involving H C F · T ds , the circulation of F along C . 2. Let F be a vector ﬁeld in R 2 deﬁned by F = - y i + x j x 2 + y 2 (a) Verify Green’s theorem over the annular region D = { ( x,y ) | a 2 x 2 + y 2 1 } . (See ﬁgure at right.) (b) Now let D be the unit disk. Does the formula of Green’s theorem hold for D ? Can you explain why? (c) Suppose C is any simple closed curve lying outside the circle C a = { ( x,y ) | x 2 + y 2 = a 2 } (see ﬁgure at right). Argue that if

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/04/2011 for the course MATH 1211 taught by Professor Wang during the Spring '11 term at HKU.

### Page1 / 2

assignment6 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online