基于介绍Lebesgue思想的实变函数论课程的教学改革研究  

On Teaching Reform of Functions of a Real Variable Based on Introducing the Lebesgue Thought

作　　者：陈建军 徐广侠 CHEN Jianjun;XU Guangxia(School of Mathematics and Statistics,Zhaoqing University,Zhaoqing,Guangdong 526061,China)

机构地区：[1]肇庆学院数学与统计学院,广东肇庆526061

出　　处：《肇庆学院学报》2021年第2期5-12,共8页Journal of Zhaoqing University

基　　金：肇庆学院博士启动项目(221622,2018010170);高等教育与基础教育的衔接问题及对策探讨(ZQJYY2018023);"新师范"背景下提升数学师范生实践教学能力培养策略实效性的研究(zlgc201862)。

摘　　要：基于介绍Lebesgue思想,本文主要探讨实变函数论课程的教学改革.不同于以往以数学史上的完备化为切入点,本文通过中学物理学中的物理模型,抽象出Dirac函数的定义,再利用Dirac函数的性质引出Riemann积分定义中的缺陷,以此介绍Lebesgue积分的思想.We mainly aim at teaching reform of Functions of a Real Variable based on the Lebesgue Thought.Instead of introducing the three mathematical completions in history,we firstly extract the definition of Dirac function by the physical model in physics of middle school,and then introduce the Lebesgue thought by analyzing the imperfections of the definition of Riemann integral which is introduced by the characteristics of Dirac function.

关 键 词：实变函数 Dirac函数 RIEMANN积分 LEBESGUE积分 

分 类 号：O171[理学—数学]