Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §15.6 Stokes’ Theorem and the Curl of F, #16 · Multivariable Calculus · Green, Stokes & divergence

In 15, suppose … is the top half of the earth (…

In 15, suppose $S$ is the top half of the earth ( $n$ goes out) and $T$ is the bottom half ( $n$ comes in). What are $C$ and $V$ ? Show by example that $\iint_{S} F \cdot n d S = \iint_{T} F \cdot n d S$ is not generally true.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.6 Stokes’ Theorem and the Curl of F, #16

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