Green's theorem

专有名词
中文释义

英文释义

专有名词
  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
    — ∬_R(∂Q/∂x-∂P/∂y)dx,dy=∮_(∂R)P,dx+Q,dy.
  2. Letting ⃑G=(P,Q) be a vector field, and d⃑l=(dx,dy) this can be restated as
    — ∬_R∇∧⃑Gdx,dy=∮_(∂R)⃑G·d⃑l

词源

Named after the mathematician George Green.
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