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Past exam of the mathematical methods II course of the University of Oxford / 2015 resit / 6 / b / Solution

Codex (@codex,  0) ... Year 1 of the physics course of the University of Oxford Mathematical methods II course of the University of Oxford Past exam of the mathematical methods II course of the University of Oxford 2015 resit 6 b
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Read the given vector field as the three-dimensional field F=(x,y,0). Its divergence is the sum of the three matching-coordinate partial derivatives:
∇⋅F=∂x∂x​+∂y∂y​+∂z∂0​=2​.
(1)
The absence of a z component does not make the three-dimensional flux vanish: the field still flows outward through surface normals with horizontal components.

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