Gauss formula, also known as divergence theorem, Gauss divergence theorem, Gauss-Ostrogradski formula or Gauss-Gauss formula, is a theorem that relates the flux of vector field passing through a surface with the expression of vector field inside the surface.

The divergence theorem can be used to calculate the flux through a closed surface, for example, any left surface; The divergence theorem cannot be used to calculate surfaces with boundaries, such as any surface on the right. In this figure, the surface is shown in blue and the boundary is shown in red. ?

The divergence theorem can be used to calculate the flux through a closed surface, for example, any left surface; The divergence theorem cannot be used to calculate surfaces with boundaries, such as any surface on the right. In this figure, the surface is shown in blue and the boundary is shown in red.

More precisely, Gaussian formula shows that the flux of vector field passing through a surface is equal to the triple integral of the divergence of the inner region of the surface. Intuitively speaking, the sum of all source points MINUS the sum of all sink points is the flow out of an area.

Gauss formula is a very important result in engineering mathematics, especially in electrostatics and fluid mechanics.

Gauss formula is expressed by divergence as:

Where σ is the boundary surface of closed space ω, and n is the projection of vector A on the external normal vector of surface σ.