assignment4

assignment4 - MATH1211/10-11(2)/A4/NKT THE UNIVERSITY OF...

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Unformatted text preview: MATH1211/10-11(2)/A4/NKT THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Assignment 4 Due date: 2011 March 14 (Monday), 5:00pm. (The Exercise/problem numbers in the following refer to those in the textbook.) 1. ( § 3.4 no.28) The Laplacian operator, denoted by ∇ 2 , is the second-order partial differential operator defined by ∇ 2 = ∂ 2 ∂x 2 + ∂ 2 ∂y 2 + ∂ 2 ∂z 2 . (a) Explain why it makes sense to think of ∇ 2 as ∇ · ∇ . (b) Show that if f and g are functions of class C 2 , then ∇ 2 ( fg ) = f ∇ 2 g + g ∇ 2 f + 2( ∇ f · ∇ g ) . (c) Show that ∇ · ( f ∇ g- g ∇ f ) = f ∇ 2 g- g ∇ 2 f. 2. ( § 4.1 no.30) If you measure the radius of a cylinder to be 2 in, with a possible error of ± . 1 in, and the height to be 3 in, with a possible error of ± . 05 in, use differentials to determine the approximate error in (a) the calculated volume of the cylinder....
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This note was uploaded on 05/04/2011 for the course MATH 1211 taught by Professor Wang during the Spring '11 term at HKU.

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assignment4 - MATH1211/10-11(2)/A4/NKT THE UNIVERSITY OF...

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