Application and Extension of Residue Theorem

Abstract

The Complex analysis is a branch of mathematics studying complex variable functions, mainly studying the properties and characteristics of complex variable functions. This paper first introduces the background and development of the residue theorem. Then this paper briefly explains the definition of the residue theorem. It also introduces the applications of residue theorem in different field of physics. The residue theorem is widely used in the integration of complex variable functions, and it is also applicable to the integration of real functions. Several examples of integral solved by the residue theorem in real variable functions are used to further understand the residue theorem and explore the application of the logarithmic residue theorem. The logarithmic residue is an important and effective method to discuss the number of poles and zeros of analytic functions. By proving and applying various inferences, the zeros and poles can be calculated efficiently and quickly, which greatly saves time for the study and applications of complex functions.