Historical synopsis of Cauchy residue theorem

This paper is aimed to discuss the importance of Cauchy residue theorem through different aspects. Firstly, we will overview Cauchy residue theorem and its proof. Then the application of Cauchy residue theorem to calculate a complicated integral of a real-valued function will be investigated. Finally, we will explore to compute the 1D Green's function for the Helmholtz equation by Cauchy residue theorem.