CAUCHY RESIDUE THEOREMS AND APPLICATIONS

ABSTRACT

Brief history, origin and relevant roles of Cauchy’s Residue Theorem in Mathematics with the help of some definitions and theorems are presented. Also, a clear picture of brief methods of calculating residues are mentioned. Some important related results (theorems) i.e. the Cauchy’s Integral Theorem, Morera’s Theorem, Cauchy’s Integral Formula, consequences of the Cauchy’s Integral formula, examples and their consequences are incorporated in this work, elaborating on what residues are, the methods of calculating residues and specifically the Cauchy’s Residue Theorem. Some of the theorems in this work has been selected carefully so that the work is useful for study in this area of research. And also applying Cauchy’s Residue Theorem to complex integral, inverse laplace transform, improper integral, trigonometric integral.