green's theorem
Word Rarity
Rare
Frequency: Zipf frequency 2.94 in modern English
19
Scrabble Score
13
Letters
3
Syllables
9
Unique Chars
Meaning
name
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
name
Letting ⃑G=(P,Q) be a vector field, and d⃑l=(dx,dy) this can be restated as
Example Sentences
- "∬_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."