基于极限概念的数学分析思路研究

Research on Mathematical Analytical Thinking Based on the Limit Concept

数学分析又叫做高级微积分,是用微积分学对函数进行深入研究的数学类别。其中,极限概念是数学分析的基础环节,也是现代数学中的一个重要内容。学习者对于极限的理解程度,不仅能够影响其在数学、物理等方面的学习水平,更影响学习者对于世界的理解程度。极限概念贯穿数学分析的始终,对于数学分析具有极强的工具性,深入研究极限概念,对于拓展数学分析思路,提升数学分析水平具有重要的意义。通过深入分析极限概念的基本内涵,提出数学分析中极限概念的应用思路,对数学分析的发展起到参考和借鉴作用。

Mathematical analysis, also known as advanced calculus, is the mathematical class which deeply studies functions by virtue of calculus. The limit concept is the basic link of mathematical analysis as well as the important content in modern mathematics. Learners＇ understanding degree toward the limit concept can not only affect their learning level in mathematics and physics, but also affect their understanding of the world. The limit concept runs throughout mathematical analysis with the strong instrumental nature. Therefore, the further study of the limit concept is of great importance to expanding the thinking of mathematical analysis as well as enhancing the level of mathematical analysis. This paper, by deeply analyzing the basic connotation of the limit concept, puts forward the thought of applying the limit concept in mathematical analysis, which can serve as the reference role for the development of mathematical analysis.