Changes

Where R is some region of 3-space, S is the boundary surface of R, the triple integral denotes volume integration over R with dV as the volume element, and the double integral denotes surface integration over S with <math>\vec{\mathrm{d}A}</math> as the oriented normal of the surface element.  The <math>\nabla \cdot</math> on the left side is the [[divergence]] operator, and the <math>\cdot</math> on the right side is the vector [[inner product|dot product]].

Where R is some region of 3-space, S is the boundary surface of R, the triple integral denotes volume integration over R with dV as the volume element, and the double integral denotes surface integration over S with <math>\vec{\mathrm{d}A}</math> as the oriented normal of the surface element.  The <math>\nabla \cdot</math> on the left side is the [[divergence]] operator, and the <math>\cdot</math> on the right side is the vector [[inner product|dot product]].

*When k=2, this is often also called '''Stokes' Theorem''' (the less general form):

*When k=2, this is often also called '''Gauss' Theorem''':

:<math>\iint_S (\nabla \times \vec w) \cdot \vec{\mathrm{d}A} = \oint_E \vec w \cdot \vec{\mathrm{d}l}\,</math>

:<math>\iint_S (\nabla \times \vec w) \cdot \vec{\mathrm{d}A} = \oint_E \vec w \cdot \vec{\mathrm{d}l}\,</math>