导数概念的教学探究

Teaching research on the concept of derivative

导数是高等数学的核心概念之一,在自然科学,工程技术和经济管理等最优化问题中有着非常广泛的应用。导数的概念具有较强的抽象性和严密的逻辑性,许多学生都未能掌握其思想和本质。为了帮助学生理解导数,在课堂教学中可先结合具有专业背景的实例和微积分发展史,引出导数的概念,激发学生的学习兴趣;再通过极限理论,完成导数概念的感性认识到理性认识的升华;最后,挖掘导数蕴含的哲学思想,培养大学生的辩证唯物主义观。

The concept of derivative is one of the most important concepts in advanced mathematics,and has a very wide range of applications in natural science,engineering technology and economic management. Because it is very abstract and logical so that many students can not understand this concept. In order to overcome the difficulty,we firstly introduce the derivative by examples of professional background and the history of calculus,secondly use the limit theory to obtain the condition of derivative,lastly explore philosophy thought of the derivative to cultivate undergraduate＇s dialectic materialistic viewpoint.