关于函数一致连续的研究性教学

Research Teaching for the Uniform Continuity

详细介绍函数一致连续的教学模式:先通过几何直观,使学生理解这一概念,随之引导学生认真学习一致连续在积分计算、函数项级数以及含参变量积分问题中的应用,使学生加深对这一概念的认识.同时就这一内容设置一系列探索性问题,进行研究性教学,以培养学生独立思考和解决问题的能力.

This paper discusses a teaching approach of the uniform continuity for functions. First, the concept is introduced through geometric intuition. Followed by some applications of the uniform continuity in integration, function series, and integral with parametric variables, a deep understanding of the concept is expected. Finally, to encourage independent thinking and to train the problem solving ability, a set of exploring problems about this concept is proposed.