From Encyclopaedia of Mathematics
edited by Michiel Hazewinkel

"The method of boundary integration consists basically of the following. Some integral is considered, taken over the entire boundary of a given domain (the boundary can generally be taken to consist of a finite number of simple closed analytic curves). This integral is chosen so that the integrand contains factors with the boundary property indicated above and such that, after using this property, an integral is obtained that can be calculated by means of the residue theorem (cf. method of Contour integration; Cauchy integral theorem)"