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assignment6

# assignment6 - MATH1211/10-11(2/A6/NKT THE UNIVERSITY OF...

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Unformatted text preview: MATH1211/10-11(2)/A6/NKT THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Assignment 6 Due date: 2011 April 21 (Thursday), 5:00pm. (The Exercise/problem numbers in the following refer to those in the textbook.) 1. ( § 6.5 no.35,36) 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 C is oriented counterclockwise, then I C xdy- y dx x 2 + y 2 = 2 π. (d) Calculate ∇ × F . (e) Evaluate H C F · d s , where C is the unit circle x 2 + y 2 = 1. (f) Is F conservative?...
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assignment6 - MATH1211/10-11(2/A6/NKT THE UNIVERSITY OF...

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