DefinitionIn the study of mathematical analysis, contour integration is a method to evaluate certain complex integrals which do not have an antiderivative. This is achieved by parameterizing the contour and applying the Cauchy integral formula or residue theorem to solve the integral. In the theory of complex functions contour integration is employed to evaluate integrals involving complex functions and relating to residues of functions and singularities. It gives a versatile way of solving integrations in both real and complex numbers, and highly applied in physics, engineering and mathematical physics. For Example: A complex function f(z) is integrated along a closed contour C in the complex plane by the residue theorem, which relates the integral to the residues of f(z) at its singular points enclosed by C.
