Surface area

The surface area of a measurable region

U \subseteq S

is

\int_{U} d A

. For a parametrization

X (u, v)

it is

\int ∣ X_{u} \times X_{v} ∣ d u d v

.

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Conservation of insoluble surfactant on a moving interface
Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 329 / 1 / Solution

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