中文摘要：

数学思想方法是数学的灵魂.主要阐述微积分中泰勒公式的应用,泰勒公式不但能用来近似计算数学常数π,而且能用来理论证明两个粗糙的近似值通过简单的组合加工技术（现代人称之为＂外推法＂）产生更准确的近似值,也把外推法推广用于求解Steklov特征值问题,数值算例表明非协调Crouzeix-Raviart有限元外推法既能提高解的精度又能提供准确特征值的下界.

英文摘要：

Mathematical thought is the soul of Mathematics.This paper mainly talks about the applications of Taylor＇s formula in Calculus.Taylor＇s formula can be not only used to compute mathematical constants like n but also used to prove that two rough approximate solutions can produce much more accurate one with the use of simple combination processing technique（called the extrapolation method）.The extrapolation method is also generalized to solve Steklov eigenvalue problems,and numerical results show that it improves the nonconforming Crouzeix-Raviart element approximation accuracy and provides the lower bounds of the exact eigenvalues.