极限概念的数学哲学思维剖析

极限是高等数学中的一个重要概念,也是学生最难于理解的概念之一。在教学中,注重产生极限概念的实际背景的介绍,分析极限定义中各个变量的变化特征与内在联系,辩证剖析变化过程中的量变与质变、近似与精确等对立统一规律,是训练和培养学生数学思维,提高综合素质和能力的重要途径之一。

On the Philosophically Mathematical Thinking of Limit

Limit is an important term in higher mathematics and also a term difficult to understand for students.In teaching,in order to train and cultivate the students' mathematical thinking and enhance their all-round qualities and abilities,we need to introduce the background of its appearance,analyze the features of quantity change and inner relationship,probe into the law of the unity of opposites,such as quantity change and quality change in changing process,approximate and accurate,and so on.