一类函数极限定义的类比探究式教学案例

Analogical Inquiry Teaching in Defining Limits

本文结合相关教学实践,介绍一元函数极限概念的探究式教学过程,在此基础上将极限相关概念和结论,运用类比与归纳方法推演到高维空间上的多元函数、向量值函数的情形,乃至进一步推广到到赋范空间、距离空间与拓扑空间上极限相关概念.

Building upon practical teaching experiences,this paper outlines an exploratory teaching approach for the concept of limits in univariate functions.Expanding from this foundation,the paper extends the understanding of limits to multivariate functions and vector-valued functions within high-dimensional spaces through analogy and induction.Moreover,it takes a step further by applying these concepts to limits within normed spaces,distance spaces,and topological spaces.