实变函数教学探讨

Discussion on Teaching Real Variable Function

摘要: 本文通过研究数学分析和实变函数共有的完备性，给出了一个类比，即相较于数学分析是把 有理数系Q推广到完备的实数系R，实变函数则是把一个不完备Riemann积分集类推广到完备的Lebesgue积分集类, 从而构建了一座从数学分析到实变函数的认知桥梁，使学生更容易接受实变函数这门课程。 同时我们还提出了要把晦涩的分析概念用简单直白的方式讲解给学生的观点，并举了一些与完备性密切相关的例子。

Abstract: This paper gives an analogy by mining the completeness of mathematical analysis and real variable functions, that is, compared with mathematical analysis, which extends the rational number system Q to the complete real number system R, real variable function extends an incomplete Riemann integral set class to the complete Lebesgue integral set class, thus we build a cognitive bridge from mathematical analysis to real variable functions. It is easy for students to accept the course of real variable function. At the same time, we also put forward the view that we should explain the obscure analytical concepts to students in a simple and straightforward way, and give some examples with completeness.