Gradient Theorem

 int_a^b(del f)·ds=f(b)-f(a),

where del 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, Poincaré's Theorem

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Gradient Theorem." From MathWorld--A Wolfram Web Resource.

Subject classifications