关于实数系的几个基本定理在“泛函分析”教学中的应用

Applications of Several Fundamental Theorems on the Real Number System in the Teaching of Functional Analysis

“泛函分析”课程通常都是大学数学专业的一门非常重要的专业主干课。然而,它作为“数学分析”“实变函数”等基础课程的后续课程具有高度综合性和抽象性的特点,这往往导致老师和学生在这门课的教与学中经常会遇到较大的困难。在本文中,结合作者多年的“数学分析”与“泛函分析”课程的教学经验与思考,我们将尝试对“泛函分析”课程的教学方法进行一定的改革探讨,以期能帮助师生最大程度地克服这种困难从而取得更好的教与学的效果。

Functional analysis is usually a very important major course.However,as the follow-up course of mathematical analysis and real variable functions,it is highly comprehensive and abstract,which leads to the big difficulty to teachers and students in the teaching and learning of this course.In this paper,combining many years’teaching experience and thinking of mathematical analysis and functional analysis,we will attempt to discuss the reform in the teaching method of functional analysis,and hope to help the teachers and students to overcome the difficulty to the most extent and achieve better teaching and learning effect.