# Divergence

In mathematics, divergence is a differential operator that associates a vector field with a scalar field. In a vector field, each point of the field is associated with a vector; in a scalar field, each point of the field is associated with a scalar.

Given a vector field ${\displaystyle \mathbf {F} }$, the divergence of ${\displaystyle \mathbf {F} }$ can be written as ${\displaystyle \operatorname {div} \mathbf {F} }$ or ${\displaystyle \nabla \cdot \mathbf {F} }$, where ${\displaystyle \nabla }$ is the gradient and ${\displaystyle \cdot }$ is the dot product operation.[1][2][3]

Divergence is used to formulate Maxwell's equations and the continuity equation.

## References

1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-10-14.
2. "Calculus III - Curl and Divergence". tutorial.math.lamar.edu. Retrieved 2020-10-14.
3. "Divergence (article)". Khan Academy. Retrieved 2020-10-14.