摘要
针对二元函数混合偏导数存在且相等,但未必连续的命题,给出反例说明.寻找反例的具体过程启示:在数学教学中,可以通过有意识的列举反例,启发学生构造反例,来培养学生的逆向思维能力,从而提高教学质量.
It is well known that if the second order mixed partial derivatives of a function of two variables are continuous inside a domain, these derivatives are identical. However, the converse is not true. Counter-examples and their constructions are useful for promoting better understanding of the fundamental concepts and theorems and students＇ reverse thinking skill.
出处
《高等数学研究》
2011年第1期95-96,共2页
Studies in College Mathematics
关键词
反例
逆向思维
二阶混合偏导数
连续
counter example, reverse thinking, second order mixed partial derivatives,continuous
