MathLiveGreen's theorem
It converts the line integral of a vector field around a positively oriented closed curve into a double integral of its curl over the region the curve encloses. It is used to evaluate line integrals in the plane or to compute areas and fluxes.
\iint_S \left( \frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y} \right) \mathrm{d}A = \oint_{\partial S} F_1 \, \mathrm{d}x + F_2 \, \mathrm{d}yWhat the symbols mean
| plane region enclosed by the closed curve | |
| boundary curve of S, oriented positively | |
| scalar function giving the x-component of the vector field | |
| scalar function giving the y-component of the vector field | |
| area element of the region S | |
| differential of x along the boundary curve \partial S | |
| differential of y along the boundary curve \partial S |
About this formula
- FieldMathematics
- TopicVector calculus
- LevelUniversity
- Also calledline integral to double integral, circulation around closed curve, green's theorem vector calculus, curl theorem in the plane, closed line integral double integral
- SourceWikidata Q321237
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