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The '''divergence''' is a way of expressing a certain type of derivative of a [[vector field]].  It is typically a field of 3-dimensional vectors defined on 3-dimensional space, but other dimensions are possible.  The divergence of a vector field is a [[scalar field]], that is, just a number at each point in space.

The '''divergence''' is a way of expressing a certain type of derivative of a [[vector field]].  It is typically a field of 3-dimensional vectors defined on 3-dimensional space, but other dimensions are possible.  The divergence of a vector field is a [[scalar field]], that is, just a number at each point in space.

The divergence is written as though it were the [[dot product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla") with the given vector field, like this: <math>\nabla \cdot \vec V</math>.  This is usually pronounced "div V" or "del dot V".

The divergence is written as though it were the [[dot product]] of the special symbol "<math>\nabla</math>" (which is commonly called "del" or "nabla"), with the given vector field, like this: <math>\nabla \cdot \vec V</math>.  This is usually pronounced "div V" or "del dot V".

In ordinary [[Cartesian coordinates]], the divergence is calculated as:

In ordinary [[Cartesian coordinates]], the divergence is calculated as: