函数一致连续性的教学探究

Teaching research on the function's uniform continuity

函数的一致连续性是数学分析中最重要,且高度抽象的概念之一,在数学分析和相关专业课的后继学习与研究中起着十分重要的作用。为了帮助学生深刻理解一致连续性的概念,首先,从连续的概念出发,形象直观地阐述一致连续性的概念;其次,从非一致连续的角度出发,进一步认识一致连续性;最后,通过揭示导函数与一致连续性的关系,深刻理解一致连续性。

The function＇ s uniform continuity, which is one of the most important and highly abstract concepts in mathematical analysis, plays an important role in studying mathematical analysis and the related specialized course. To help students understand the concept of uniform continuity, we visually described it on the basis of the concept of continuity, and two examples of nonuniform continuity were presented, and then the relation between the derived function and the uniform continuity were drawn out.