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  1. Verify the divergence theorem for the function $\textbf{V} = xy \textbf{i} - y^2 \textbf{j} + z \textbf{k}$ and the surface enclosed by the three parts (i) $z = 0, s < 1, s^2 = x^2 + y^2$, (ii) $s = 1, 0 \le z \le 1$ and (iii) $z^2 = a^2 + (1 - a^2)s^2, 1 \le z \le a, a > 1$.

Normally questions like these wouldn't pose a problem for me. However, I am having trouble interpreting the surfaces being described. Hopefully someone can shed some light on this.

NormalsNotFar
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    (i) open disc in $z=0$ plane; (ii) cylinder with unit radius and unit height; (iii) half of the ellipsoid (put $s^2$ term on the lhs and divide by $a^2$) – Ivica Smolić Jan 18 '16 at 17:57

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I would assume that $s^2 = x^2 + y^2$ applies to all three parts and that $a$ is a fixed constant greater than $1$. Then (i) describes a disk in the $xy$-plane, (ii) describes a cylinder of height $1$ and radius $1$, and (iii) describes (part of) an ellipsoid.

Michael Joyce
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