两个关于幂级数及其和函数收敛性问题的教学探讨

Two Teaching Discussions on the Convergence of Power Series and Their Sum Functions

摘要: 幂级数及其和函数的性质是高等数学教学中的难点之一。本文主要探讨日常教学实践中遇到的问题。通过讨论发现，核心问题源于对和函数定义的误解。因此，作者认识到重视学生提出的问题的重要性，并尝试采用适当方法解答疑问，从而提升课堂教学效果。同时，这一过程也有助于教师改进教学技能，并培养高等数学教学中概念意象渗透原则的意识。

Abstract: Power series and the properties of their sum functions represent one of the challenging teaching points in advanced mathematics. This article primarily discusses issues encountered during routine teaching practice. Through discussion, it was discovered that the core issue stems from a misunderstanding of the definition of the sum function. Consequently, the author recognizes the importance of valuing questions raised by students and attempts to use appropriate methods to address their queries, thereby enhancing classroom teaching effectiveness. Simultaneously, this process also helps teachers improve their teaching skills and fosters an awareness of the permeation of the concept imagery principle in advanced mathematics instruction.