In vector calculus, divergence is an operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. For example, consider air as it is heated or cooled. The relevant vector field for this example is the velocity of the moving air at a point. If air is heated in a region it will expand in all directions such that the velocity field points outward from that region. Therefore the divergence of the velocity field in that region would have a positive value, as the region is a source. If the air cools and contracts, the divergence is negative and the region is called a sink.
Định nghĩa của divergence rất khó hiểu như sau:
More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,
Let x, y, z be a system of Cartesian coordinates on a 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.
The divergence of a continuously differentiable vector field F = U i + V j + W k is equal to the scalar-valued function:
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