Word.ws English Dictionary

Green's theorem

Green's theorem proper noun: 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.

Proper noun

Green's theorem

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

Origin of Green's theorem

Named after the mathematician George Green.

Questions about Green's theorem

What does Green's theorem mean?
Green's theorem means 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.
What part of speech is Green's theorem?
Green's theorem is a proper noun.

Words near Green's theorem in the dictionary

  1. green yards
  2. Green Zionism
  3. green zone
  4. Green's function
  5. Green's functions
  6. Green's theorem
  7. green-backed
  8. green-backed firecrown
  9. green-backed firecrowns
  10. green-backed flycatcher
  11. green-backed flycatchers

Source and license

Adapted from Wiktionary: Green's theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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