| 柯西积分定理的初等证明 |
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| 引用本文： | 王信松,张节松. 柯西积分定理的初等证明[J]. 安徽大学学报(自然科学版), 2011, 35(5): 6-9 |
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| 作者姓名： | 王信松 张节松 |
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| 作者单位： | 1. 天津城市建设学院基础学科部,天津,300384
2. 淮北师范大学数学科学学院,安徽淮北,235000 |
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| 基金项目： | 安徽省教育厅自然科学基金资助项目(2006KJ069A) |
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| 摘 要： | 利用数学分析的知识构造一个简单的恒同逼近函数,由此用分析中的逼近思想,成功地用满足柯西-黎曼条件的连续可微的函数逼近一般的可微函数,给出了柯西积分定理的一个初等证明,克服了复变函数论中这一关键性定理证明繁琐或者超纲的困难.
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| 关 键 词： | 解析函数 柯西积分定理 单连同区域 |
Elementary proof of Cauchy integral theorem |
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| WANG Xin-song,ZHANG Jie-song. Elementary proof of Cauchy integral theorem[J]. Journal of Anhui University(Natural Sciences), 2011, 35(5): 6-9 |
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| Authors: | WANG Xin-song ZHANG Jie-song |
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| Affiliation: | 1.Department of Basic Course,Tianjin Institute of Urban Construction,Tianjin 300384,China; 2.School of Mathematics Science,Huaibei Normal University,Huaibei 235000,China) |
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| Abstract: | In this paper,a simple identity approximation function was constructed by using the knowledge of mathematic analysis,thereby,applying the approximation idea in analysis,we successfully obtained that ordinary differential functions were well approximated by continuously differentiable functions satisfying the Cauchy-Riemann equations,and an elementary proof of Cauchy integral theorem was presented,which overcame some troublesome or over-syllabus difficulties in the proof of the theorem in the text of complex variable functions,and was also beneficial to the teaching. |
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| Keywords: | analytic functions Cauchy integral theorem simply connected domain |
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