“等价无穷小替换”求极限的教学思考

On Teaching in Finding Limit in Equivalent Infinitesimal Replacement

《高等数学》在大学非数学专业中是一门非常重要的数学类基础课程,极限的思想贯穿了整门课程,其中,等价无穷小替换是求极限的基本方法之一.该文从把握重要概念和基本原理的实质、改革教学方法和手段、对原理的应用实施分类教学、训练一题多解、解决问题抓主要方面、合理利用教学中的错误资源等几个方面进行思考,让初学者有更清晰的理解并掌握这门课程.

Advanced Mathematics is a very important basic subject of mathematics for non-mathematics majors in universities.The thought of limit has been applied in the whole subject,among which the Equivalent Infinitesimal Replacement is one of the basic methods of finding the limit.This paper deals with the thought in the following aspects,such as the grasp of the essence of important concepts and the basic principle,the reform of teaching methods and means,the implementation of classification teaching in the application of the principle,training of one problem with more solutions and the ability to solve problems by grasping the main aspects,the errors in the rational utilization of teaching resources and etc.The purpose is to let the beginners have a clearer understanding and mastering of this knowledge point.