Quiz 4 Solution

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Unformatted text preview: , y ) = ∇ × G, if it exists. Solution: Since the vector field is C 1 on all of R3 and ∇·(x2 + 1, z − 2xy, y ) = 0 then G exists. Let G (x, y, z ) = (G1 , G2 , G3 ) and try setting G3 = 0. ˆ ı ∇×G= ˆ ˆ k ∂ ∂x ∂ ∂y ∂ ∂z G1 G2 0 = x2 + 1, z − 2xy, y . Math 3010 Quiz 4 Nov. 28, 2012 This yields the following system: ∂G2 = x2 + 1, ∂z ∂G1 = z − 2xy, ∂z ∂G2 ∂G1 − = y. ∂x ∂y − Integrating the first and second equations with respect to z yields G1 (x, y, z ) = z2 − 2xyz + g1 (x, y ) ,...
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This note was uploaded on 01/19/2014 for the course MATH 3010 taught by Professor Magpantay during the Winter '13 term at York University.

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