| 以一元函数到多元函数为例论证从量变到质变的变化过程 |
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| 引用本文： | 慕运动,张德洋.以一元函数到多元函数为例论证从量变到质变的变化过程[J].数学学习,2020(2):59-62,F0003. |
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| 作者姓名： | 慕运动 张德洋 |
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| 作者单位： | 河南工业大学理学院 |
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| 基金项目： | 河南省教学研究课题(2017SJGLX295)(GJYJ-ZB11)。 |
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| 摘 要： | 本文结合一元函数和多元函数来讨论哲学中的最基本的质量互变规律——事物发生质变的前提是存在量变的积累过程.根据一元函数和多元函数在微积分中的逻辑关系来找出关键的不同点,结合质量互变规律找出两者之间的联系,以及分析这种质变的来源究竟是何种量变引起.从而体现质量互变规律在数学中的应用,也肯定哲学思想对数学的促进作用,达到启迪数学学习和数学教育的作用.
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| 关 键 词： | 量变 质变 函数 极限 教学 |
Demonstrating Mutual Transformation of Quantity and Quality by One-variable and Multivariate Functions |
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| MU Yundong,ZHANG Deyang.Demonstrating Mutual Transformation of Quantity and Quality by One-variable and Multivariate Functions[J].Studies In College Mathematics,2020(2):59-62,F0003. |
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| Authors: | MU Yundong ZHANG Deyang |
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| Institution: | (College of Science, Henan University of Technology, Zhengzhou 450001, China) |
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| Abstract: | This paper demonstrates the basic law of the mutual transformation of quantity and quality in philosophy by functions of one-variable and multi-variable.According to the logical relationship between one-variable and multi-variable functions,key differences are found,and the relationships between them are identified based on the law.By analyzing the source of the qualitative change,we confirm the application of the law in mathematics and the role of philosophical thought in promoting mathematics so as to enlighten mathematics learning and mathematics education. |
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| Keywords: | quantitative change qualitative change function limit teaching |
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