| 柯西-许瓦兹不等式的证明方法及应用 |
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| 引用本文： | 张二艳,张永明.柯西-许瓦兹不等式的证明方法及应用[J].北京印刷学院学报,2012,20(2):71-73. |
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| 作者姓名： | 张二艳 张永明 |
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| 作者单位： | 北京印刷学院基础部,北京,102600;北京印刷学院基础部,北京,102600 |
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| 基金项目： | 北京市属高等学校人才强教计划资助项目(PHR201107145) |
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| 摘 要： | 柯西-许瓦兹不等式在数学竞赛和数学分析的不等式证明中具有广泛应用,证明方法也非常灵活。利用判别式、作差比较、向量和二次型等方法给出4种证明方法及应用。在不同的教学场合,根据不同的需要和可能,灵活地使用合适的证明方法,从而加深对该不等式的理解,利于教学。
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| 关 键 词： | 柯西-许瓦兹不等式 判别式 作差比较 向量 二次型 证明 |
Proof Methods and Applications of Cauchy-Schwartz Inequality |
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| ZHANG Er-yan,ZHANG Yong-ming.Proof Methods and Applications of Cauchy-Schwartz Inequality[J].Journal of Beijing Institute of Graphic Communication,2012,20(2):71-73. |
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| Authors: | ZHANG Er-yan ZHANG Yong-ming |
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| Affiliation: | (Beijing Institute of Graphic Communication,Beijing 102600,China) |
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| Abstract: | Cauchy-Schwartz inequality in mathematics competition and mathematical analysis of the inequality proof method has wide application which is very flexible.Using discriminate of quadratic function method makes difference comparison method,vector method and the quadratic form the given method and it is the four kind of proof method and applications.In different teaching situations,according to different needs and may,the flexible use of appropriate methods is proven inequality,so as to enhance the understanding and teaching. |
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| Keywords: | Cauchy-Schwartz Inequality discriminate vector make difference comparison quadratic form proof |
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