摘要
极限与无穷小是微积分中的基本概念,是整个微积分学的理论基础.极限是运动与静止的统一;极限可以被看作是函数变换器;极限是连接有限与无限的桥梁.极限与无穷小有着密切的关系,借助于极限,可以深刻地理解无穷小的本质.反过来,无穷小思想也是对极限思想的补充.深刻地理解极限和无穷小的实质,对学习微积分是十分必要的.
Limit and infinitesimal are basic concepts of calculus, and are the theoretical basis of the calculus. The limit is the unity of the dynamic and the static. It can be seen as a function converter like a bridge which connects finite and infinite. With the help of the limit, we can clearly understand the essence of the infinitesimal. On the contrary, the infinitesimal theory is a supplement to the limit theory. A profound understanding of the essence of limit and infinitesimal is essential to the study of Calculus.
关键词
极限
变换
无穷小
微元法
limit
transform
infinitesimal
micro-element method
