毕业论文 不等式的若干证明方法--定理的应用.doc
约22页DOC格式手机打开展开
毕业论文 不等式的若干证明方法--定理的应用,摘要无论在初等数学还是高等数学中,不等式都是十分重要的内容.而不等式的证明则是不等式知识的重要组成部分.在本文中，我总结了一些数学中证明不等式的方法.在初等数学不等式的证明中经常用到的有比较法、作商法、分析法、综合法、数学归纳法、反证法、放缩法、换元法、判别式法、函数法、几何法等等.在高等数学不等式的证明中经常利用中值...
内容介绍
此文档由会员 ljjwl8321 发布
摘 要
无论在初等数学还是高等数学中,不等式都是十分重要的内容.而不等式的证明则是不等式知识的重要组成部分.在本文中，我总结了一些数学中证明不等式的方法.在初等数学不等式的证明中经常用到的有比较法、作商法、分析法、综合法、数学归纳法、反证法、放缩法、换元法、判别式法、函数法、几何法等等.在高等数学不等式的证明中经常利用中值定理、泰勒公式、拉格朗日函数、以及一些著名不等式，如：均值不等式、柯西不等式、詹森不等式、赫尔德不等式等等.从而使不等式的证明方法更加的完善，有利于我们进一步的探讨和研究不等式的证明. 通过学习这些证明方法，可以帮助我们解决一些实际问题，培养逻辑推理论证能力和抽象思维的能力以及养成勤于思考、善于思考的良好学习习惯.
关键词：不等式；比较法；数学归纳法；函数等等
Abstract
No matter in elementary maths or higher in mathematics, inequality is very important content. The inequality proof is an important part of the inequality knowledge. In this paper, I summarized some mathematical proof of inequality technique. In elementary mathematics inequality for the evidence is often used as a comparison, the commercial law, analysis and synthesis, mathematical induction, reduction, zooming method, in yuan method, discriminant method, function method, geometric method, etc. In the higher mathematics inequality for often use the evidence of the mean value theorem, Taylor formula, Lagrange function, and some famous inequality, such as: mean, inequality cauchy inequality, Jason, inequality holder inequation, etc. So that inequality proof of the method is more perfect, be helpful for our further research and study of the inequality proof. By studying the identification method, can help us solve some practical problems, cultivate logical reasoning ability and the abstract thinking ability, and develop thinking, good at thinking of the good study habits.
Keywords: inequality; Comparison method; Mathematical induction; Function and so on .
目录
摘要……………………………………………………………………1
Abstract………………………………………………………………2
0引言 …………………………………………………………………4
1利用函数证明不等式
1.1函数极值法…………………………………………………5
1.2单调函数法…………………………………………………5
1.3中值定理法…………………………………………………6
1.4利用拉格朗日函数法………………………………………6
2利用著名不等式
2.1利用均值不等式……………………………………………8
2.2利用柯西不等式……………………………………………9
2.3利用赫尔德不等式…………………………………………9
2.4利用詹森不等式……………………………………………10
3利用积分不等式的性质
3.1积分不等式的性质…………………………………………11
3.2积分不等式的证明…………………………………………12
参考文献………………………………………………………………20
致谢……………………………………………………………………21
无论在初等数学还是高等数学中,不等式都是十分重要的内容.而不等式的证明则是不等式知识的重要组成部分.在本文中，我总结了一些数学中证明不等式的方法.在初等数学不等式的证明中经常用到的有比较法、作商法、分析法、综合法、数学归纳法、反证法、放缩法、换元法、判别式法、函数法、几何法等等.在高等数学不等式的证明中经常利用中值定理、泰勒公式、拉格朗日函数、以及一些著名不等式，如：均值不等式、柯西不等式、詹森不等式、赫尔德不等式等等.从而使不等式的证明方法更加的完善，有利于我们进一步的探讨和研究不等式的证明. 通过学习这些证明方法，可以帮助我们解决一些实际问题，培养逻辑推理论证能力和抽象思维的能力以及养成勤于思考、善于思考的良好学习习惯.
关键词：不等式；比较法；数学归纳法；函数等等
Abstract
No matter in elementary maths or higher in mathematics, inequality is very important content. The inequality proof is an important part of the inequality knowledge. In this paper, I summarized some mathematical proof of inequality technique. In elementary mathematics inequality for the evidence is often used as a comparison, the commercial law, analysis and synthesis, mathematical induction, reduction, zooming method, in yuan method, discriminant method, function method, geometric method, etc. In the higher mathematics inequality for often use the evidence of the mean value theorem, Taylor formula, Lagrange function, and some famous inequality, such as: mean, inequality cauchy inequality, Jason, inequality holder inequation, etc. So that inequality proof of the method is more perfect, be helpful for our further research and study of the inequality proof. By studying the identification method, can help us solve some practical problems, cultivate logical reasoning ability and the abstract thinking ability, and develop thinking, good at thinking of the good study habits.
Keywords: inequality; Comparison method; Mathematical induction; Function and so on .
目录
摘要……………………………………………………………………1
Abstract………………………………………………………………2
0引言 …………………………………………………………………4
1利用函数证明不等式
1.1函数极值法…………………………………………………5
1.2单调函数法…………………………………………………5
1.3中值定理法…………………………………………………6
1.4利用拉格朗日函数法………………………………………6
2利用著名不等式
2.1利用均值不等式……………………………………………8
2.2利用柯西不等式……………………………………………9
2.3利用赫尔德不等式…………………………………………9
2.4利用詹森不等式……………………………………………10
3利用积分不等式的性质
3.1积分不等式的性质…………………………………………11
3.2积分不等式的证明…………………………………………12
参考文献………………………………………………………………20
致谢……………………………………………………………………21
