《数学分析》教学过程中容易被忽视的环节的教学探讨

Teaching Research on Some Knowledge of 《Mathematical analysis》 Which Are Easy to Be Overlooked

国内大部分高等院校数学专业使用华东师大版的《数学分析》作为教材.在教学实践中,发现教材有一些重要的环节没有处理好,容易被教师忽略.本文从凹凸函数的连续性、微积分学基本定理、牛顿-莱布尼茨公式和定积分分部积分法、泰勒级数的和函数、多元函数的极值与最值问题、多元函数的可微性充分条件、有界图形面积为零的充要条件等多方面指出了教材的一些瑕疵,分析了存在的问题,并根据教学实践给出了教学建议.

The textbook《Mathematical analysis》was used widely in Chinese colleges and universities.In our practice,we find that there are some defects in this textbook which may be overlooked by teachers.This paper is devoted to analyze the deficiencies such as the continuity of convex function、fundamental theorem of the calculus、Newton- Leibniz formula and integration by part,the sum function of Taylor series,extremum and maximum problem in multivariate function,sufficient condition of differentiable of multivariate function,area of bounded graphics,and so on.We also provide suggestions on how to teach these topics.