In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal neighborhood of each point.

4 days ago · In this section, we examine two important operations on a vector field: divergence and curl. They are important to the field of calculus for several reasons, including the use of curl and …

Nov 16, 2022 · In this section we will introduce the concepts of the curl and the divergence of a vector field. We will also give two vector forms of Green’s Theorem and show how the curl can be used to …

The divergence of a vector field allows us to return a scalar value from a given vector field by differentiating the vector field. In this article, we’ll cover the fundamental definitions of divergence.

Divergence is an operation on a vector field that tells us how the field behaves toward or away from a point. Locally, the divergence of a vector field F in R 2 or R 3 at a particular point P is a measure of …

The divergence of a vector field measures the density of change in the strength of the vector field. In other words, the divergence measures the instantaneous rate of change in the strength of the vector …

Oct 25, 2025 · Divergence is a vector calculus operator that measures the magnitude of a vector field's source or sink at a given point. In other words, it quantifies how much a vector field spreads out …

Jul 15, 2025 · The gradient points in the direction of the steepest increase of a scalar field, the divergence tells us how much a vector field spreads out from or converges to a point, and the curl …

Generally, the divergence of a vector field results in a scalar field (divergence) that is positive in some regions in space, negative other regions, and zero elsewhere.

Dec 3, 2025 · A formula for the divergence of a vector field can immediately be written down in Cartesian coordinates by constructing a hypothetical infinitesimal cubical box oriented along the …