One page for each problem (a total of 2 pages). 50 % Penalty if not followed.
Make a single PDF file. File name: hw_06_doe_john.pdf.
Email the PDF file to me5331exam@gmail.com with the subject line: Doe, John, HW#6
1.
Remember that the definition of divergence operator (in 2-D) is
divv ≡
lim
∆S→ 0
⌠ ⌡
∂S
n·vdl
∆S
,
(1)
where n is the normal to the boundary
and ∆S is the area of an object and the integral range is over
the contour (boundary) of the area.
Evaluate the above for
v = (xy, x + y)
defined over the circle, x2 + y2 = ϵ2, and compute the limit by letting ϵ→ 0.
Also compare this value with directly computing div v at (0, 0).
2.
Compute
⌠ (⎜) ⌡
√
x2 + 4 y2 + 9 z2
dS,
where the integral range, S, is the surface of an ellipsoid given by
x2 + 2 y2 + 3 z2 = 1.
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