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单词 surface integral
释义

surface integral

For a smooth surface Σ, and continuous (see continuous function) scalar field f on Σ and a continuous vector field F on Σ, a surface integral may take either of the forms inline or inline. If f is identically 1, then the integral inline defines the surface area of Σ. The integralinline defines the flux of F through Σ. If r(u,v), where (u,v) ε U ⊆ R2, is a parametrization of Σ, then the surface integrals are defined by

where × denotes the vector product. See divergence theorem, Stokes' theorem.

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更新时间:2025/4/29 11:42:06