(Q116938950)

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surface integral of a vector field

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vector surface integral

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Statements

subclass of

surface integral

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defining formula

\iint _{S}{\boldsymbol {F}}\cdot \mathrm {d} {\boldsymbol {\sigma }}=\iint _{D}{\boldsymbol {F}}({\boldsymbol {\Phi }}(u,v))\cdot \left({\frac {\partial {\boldsymbol {\Phi }}(u,v)}{\partial u}}\times {\frac {\partial {\boldsymbol {\Phi }}(u,v)}{\partial v}}\right)\,\mathrm {d} u\,\mathrm {d} v

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in defining formula

\iint _{S}{\boldsymbol {F}}\cdot \mathrm {d} {\boldsymbol {\sigma }}

symbol represents

surface integral of a vector field

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{\boldsymbol {F}}

symbol represents

vector field

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S

symbol represents

parametric surface

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\iint _{D}f(u,v)\,\mathrm {d} u\,\mathrm {d} v

symbol represents

double integral

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{\boldsymbol {\Phi }}

symbol represents

surface parameterization

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\cdot

symbol represents

scalar product

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{\frac {\partial }{\partial x}}

symbol represents

partial derivative

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\times

symbol represents

vector product

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

Digital Library of Mathematical Functions ID

1.6.E55

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enwiki Surface integral of a vector field

(Q116938950)

surface integral of a vector field

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