See Green's theorem on Wiktionary
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{
"text": "∬_R(∂Q/∂x-∂P/∂y)dx,dy=∮_(∂R)P,dx+Q,dy."
}
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"A generalization of the fundamental theorem of calculus to the two-dimensional plane, which states that given two scalar fields P and Q and a simply connected region R, the area integral of derivatives of the fields equals the line integral of the fields, or"
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"(calculus) A generalization of the fundamental theorem of calculus to the two-dimensional plane, which states that given two scalar fields P and Q and a simply connected region R, the area integral of derivatives of the fields equals the line integral of the fields, or"
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"text": "∬_R∇∧⃑Gdx,dy=∮_(∂R)⃑G·d⃑l"
},
{
"text": "where ∧ is the wedge product, or equivalently, as\n∬_R∇·⃑Gdx,dy=∮_(∂R)⃑G∧d⃑l,"
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"text": "with the earlier formula resembling Stokes' theorem, and the latter resembling the divergence theorem."
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"Letting ⃑G=(P,Q) be a vector field, and d⃑l=(dx,dy) this can be restated as"
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"(calculus) Letting ⃑G=(P,Q) be a vector field, and d⃑l=(dx,dy) this can be restated as"
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"etymology_text": "Named after the mathematician George Green.",
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Download raw JSONL data for Green's theorem meaning in All languages combined (3.0kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-06-05 from the enwiktionary dump dated 2025-06-01 using wiktextract (5ee713e and f1c2b61). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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