无穷小的局部有界性在直觉思维培养中的应用  

Application of infinitesimal local boundedness in the training of intuitive thinking

作　　者：易华[1] 王新长[1] 雷南燕 

机构地区：[1]井冈山大学数理学院,江西吉安343009

出　　处：《新余学院学报》2014年第4期31-33,共3页Journal of Xinyu University

基　　金：井冈山大学博士科研启动项目(自然科学)(JZB1304)

摘　　要：极限理论的诞生使无穷小理论得以严密化。在数学学习与教学中,兼顾数学思想方法的直观性与严密性的学习模式有助于对数学概念、方法的掌握和理解。对无穷小的直观理解可以启迪学生思考,而无穷小理论的严密化可以验证这些思路,进而,学生可以对这类问题有一个完整的知识框架。通过研究无穷小的直观性与严密性在数学学习中的应用,可为这种学习模式提供一种思路。Limit theory （namely language） laid the foundation of the infinitesimal theory. However, before the founding of the theory, the intuitive understanding and cognition of infinitesimal has brought fruitful results for natural science. In mathematics learning and teaching, the learning model combining both intuitive understanding and unassailable logics can make for the mastery and understanding of mathematical concepts and methods. On the one hand, the intuitive thinking for the infinitesimal can enlighten students, on the other hand, the thinking can be tested by demonstration. In this paper, the application of intuition and logics of the infinitesimal in mathematics learning is studied. Some examples are given to illustrate this learning model.

关 键 词：无穷小 局部有界性 直觉思维 

分 类 号：O141.4[理学—数学]