Divergence theorem
Teorema de la divergencia
- Date
- 1762 (Lagrange) / 1826 (primera demostración general, Ostrogradski) · confidence medium
- Place
- Paris, France
- Credited to
- Mikhail Ostrogradsky (first general proof); building on Lagrange (1762), Gauss (1813) and Green (1828)
- Field
- Knowledge & symbols
What was discovered
Studying in Paris under Cauchy, Laplace and Poisson, Ukrainian mathematician Ostrogradsky presented to the Academy of Sciences the first general proof of the theorem relating the flux of a vector field through a closed surface to the field's divergence in the enclosed volume, applying it to the study of heat flow. Lagrange, Gauss and Green had earlier proved particular cases of the same result.
The result is known variously as Gauss's theorem, Ostrogradsky's theorem or, in the planar case, Green's theorem, because several mathematicians proved particular cases before Ostrogradsky's general proof.
What it led to
- Maxwell's equations of electromagnetism
- Integral theorems of vector calculus (Green, Stokes)
Built on
- Multivariable integral calculus