Gradient theorem

Let $\phi \left(\mathbf {r} \right)$ be a scalar field.

Let L be a curve from p to q.

Then the gradient theorem says that

$\phi \left(\mathbf {q} \right)-\phi \left(\mathbf {p} \right)=\int _{L}\nabla \phi \cdot \mathbf {r}$

See also: solenoidal field, stokes theorem