The residue theorem is an important theorem in the mathematical physics methods, which is a compulsory course of physics major in college． The teaching of this theorem in traditional teaching focuses only on the derivation of mathematical formulas and the transmission of mathematics thoughts, but it is rarely involved in its application in specific physical problems． Taking the problem of the topological phase transition in one-dimensional Su-Schrieffer-Heeger model as an example, one explains how to use the residue theorem to analytically obtain the expression of the second-order displacement and use this physical quantity to characterize the topological phase transition． Introducing the analysis examples of specific physical problems in the teaching process of the residue theorem can enable students to understand the physical connotation of mathematical theorems more deeply．