Meaning of Green's theorem | Babel Free

Definitions

1. 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
2. Letting ⃑G=(P,Q) be a vector field, and d⃑l=(dx,dy) this can be restated as

Equivalents

Examples

“∬_R(∂Q/∂x-∂P/∂y)dx,dy=∮_(∂R)P,dx+Q,dy.”

“∬_R∇∧⃑Gdx,dy=∮_(∂R)⃑G·d⃑l”

“where ∧ is the wedge product, or equivalently, as ∬_R∇·⃑Gdx,dy=∮_(∂R)⃑G∧d⃑l,”

“with the earlier formula resembling Stokes' theorem, and the latter resembling the divergence theorem.”

CEFR level