如何破解极限定义教学难题

How to Solve the Problem of Teaching of Limit Definition

微积分是理工科的基础课程,学好微积分对后续课程的学习以及对学生专业素质的培养都具有十分重要的意义.而极限是微积分的基石,因为极限的思想和方法是解决微积分问题的工具.极限定义教学是整个微积分教学的重点和难点,是学生学习大学数学的一道障碍.提出了＂9个结合＂破解极限定义教学难题的综合性方法：感性与理性相结合;现象与本质相结合;数与形相结合;分析与综合相结合;正面与反面相结合;数列极限与函数极限相结合;理论与实践相结合;传统与现代相结合;内因与外因相结合.

Calculus is the foundation of science and engineering courses.It＇s of great significance to learn calculus well on the learning of follow-up courses as well as the training of professional quality.The limit is the cornerstone of calculus,because the thinking and methods of limit is a tool to solve calculus problems.The limit definition teaching is an important and difficult part in the whole teaching of calculus,as well as an obstacle for college students to learn college mathematics.Some important comprehensive methods to solve the problems of limit definition teaching are presented,which are nine combinations： combination of emotion and ration;combination of phenomenon and nature;combination of algebra and geometry;combination of analysis and synthesis;combination of positive situation and negative situation;combination of sequence limit and function limit;combination of theory and practice;combination of tradition and modern times;combination of internal cause and external cause.