More precisely, the divergence at a point is the rate that the flow of the vector field modifies a volume about the point in the limit, as a small volume shrinks down to the point. As an example, consider air …

Dec 11, 2025 · 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 …

An alternative notation for divergence and curl may be easier to memorize than these formulas by themselves. Given these formulas, there isn't a whole lot to computing the divergence and curl.

Oct 25, 2025 · Divergence and Curl are differential operators in vector calculus. The divergence is a scalar operator applied to a 3D vector field, while the curl is a vector operator that measures the …

Roughly speaking, divergence measures the tendency of the fluid to collect or disperse at a point, and curl measures the tendency of the fluid to swirl around the point. Divergence is a scalar, that is, a …

The divergence operator is defined and explained on this page. Divergence takes a vector input and returns a scalar output.

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 …

Jul 15, 2025 · Learn about the gradient, curl, and divergence in vector calculus and their applications.

An example of computing and interpreting the divergence of a two-dimensional vector field.

Generally, divergence explains how the field behaves towards or away from a point. Similarly, curl is used to measure the rotational extent of the field about a particular point.