Gradient Theorem

$$\int_b^a (\nabla f)\cdot d{\bf s} = f(b)-f(a),$$

where $\nabla$ is the Gradient, and the integral is a Line Integral. It is this relationship which makes the definition of a scalar potential function $f$ so useful in gravitation and electromagnetism as a concise way to encode information about a Vector Field.

See also Divergence Theorem, Green's Theorem, Line Integral