STOKES’ THEOREM

Abstract

Here curlnF(P) is defined as follows. Let P ∈ R3 and n be a unit vector and let S be a surface through P having normal n at P. Consider a closed curve C contained in S and circulating counterclockwise around the point P, and let A be the area of the portion of surface enclosed by C. Then curlnF(P) is the limit of the ratio between the line integral of F over C over the area of A when C shrinks to P, that is,