| 微积分中几个著名病态函数的理解与分析 |
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| 引用本文： | 周高军,郑宝杰.微积分中几个著名病态函数的理解与分析[J].河南教育学院学报(自然科学版),2014(4):35-37. |
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| 作者姓名： | 周高军 郑宝杰 |
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| 作者单位： | 河南教育学院数学与统计学院; |
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| 基金项目： | 河南省软科学项目(132400410105);河南省教师教育研究课题(2013-JSJYYB-116) |
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| 摘 要： | 简要介绍了微积分中4个著名病态函数的历史及其重要性质.对这些函数的了解,一方面可以认识到病态函数在微积分的发展过程中所起的重要作用,另一方面还可以进一步增强对微积分中某些重要概念及结论的理解.
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| 关 键 词： | 病态函数 Dirichlet函数 Cauchy函数 Riemann函数 Weierstrass函数 |
The Understanding and Analysis on Several Well-known Pathological Functions in Calculus |
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| ZHOU Gao-jun,ZHENG Bao-jie.The Understanding and Analysis on Several Well-known Pathological Functions in Calculus[J].Journal of Henan Education Institute(Natural Science Edition),2014(4):35-37. |
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| Authors: | ZHOU Gao-jun ZHENG Bao-jie |
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| Institution: | (Department of Mathematics and Statistic, Henan Institute of Education, Zhengzhou 450046, China) |
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| Abstract: | Four well-known pathological functions in calculus are discussed, and both the history and the important property of the functions are introduced. The functions have double purposes： on the one hand, they allow us to un- derstand the important role of the pathological functions in the development of calculus ; on the other hand, they ean also further enhance our understanding of the corresponding concepts and conclusions in calculus. |
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| Keywords: | pathological function Dirichlet function Cauchy function Riemann function Weierstrass function |
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