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{{math-h}}

{{math-h}}

The '''divergence''' is a way of expressing a certain type of [[derivative]] of a [[vector field]].  It is typically defined for fields of 3-dimensional vectors 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.  Vector fields with a divergence of zero are called ''divergenceless'' or ''solenoidal''.

The '''divergence''' is a way of expressing a certain type of [[derivative]] of a [[vector field]].  It is typically defined for fields of 3-dimensional vectors 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.  Vector fields with a divergence of zero are called ''incompressible'' or ''solenoidal''.

Strictly speaking, The divergence of a Vector Field '''F''' is defined as the limit of the surface integral as the volume shrinks to 0:

Strictly speaking, The divergence of a vector field '''F''' is defined as the limit of the surface integral as the volume shrinks to 0:

:<math>\operatorname{div}\,\mathbf{F} = \lim_{V \rightarrow 0} \frac{ \oint_\mathbf{S} \mathbf{F} \cdot d\mathbf{a} }{V}</math>

:<math>\operatorname{div}\,\mathbf{F} = \lim_{V \rightarrow 0} \frac{ \oint_\mathbf{S} \mathbf{F} \cdot d\mathbf{a} }{V}</math>