Divergence Theorem
A fundamental theorem of vector calculus stating that the outward flux of a vector field through a closed surface ∂V equals the volume integral of its divergence over the enclosed region V.
Governing formula
∯_(∂V) F · dA = ∭_V (∇ · F) dV
SI unit
Vector Integral Theorem
In depth
Also known as Gauss's theorem. Equates boundary surface flux to interior field sources, converting Gauss's electrostatic law from integral to differential form (∇ · E = ρ/ε₀).
Examples in the real world
Converting integral conservation laws of mass and charge into differential continuity equations in fluid dynamics and electrodynamics.