Green's theorem

短语

发音

US

释义与例句

name
  1. 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

    数学
  2. 2.

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

    数学

    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.

词源

Named after the mathematician George Green.

来源：wiktionary