毕业论文不等式的证明与应用.doc

本科毕业设计（论文） 不等式的证明与应用 学 院______应用数学学院___ 专 业______信息与计算科学__ 年级班别______2010级（2）班__ （信息计算方向） 学 号___ 3110008342______ 学生姓名______王清林_______ 指导教师 李建平 2014年月日Abstract Inequality is very important in mathematics, inequality and proof is an important part of knowledge. In this paper, the elementary mathematics inequality analyst is often used with comparison method, synthetic method, analysis method, the reduction to absurdity, zoom method, mathematical induction, change element method, construction method and so on. In higher mathematics inequality analyst frequently use some famous inequalities, such as: average inequality, cauchy inequality, Jensens inequality,holder inequality, inequality of absolute value, Bernoulli inequality and so on. By studying these proofs, can help us to solve some problems in practical application. Key words inequality; comparison method; famous inequalities; application 目 录 1 绪论……………………………………………………………………………………….1 1.1 不等式的研究背景…………………………………………………………………..1 1.2 不等式的研究方法和目的…………………………………………………………..3 1.3 论文的研究内容……………………………………………………………………..4 2 不等式及其性质………………………………………………………………………….5 2.1 不等式的基本概念…………………………………………………………………..5 2.2 不等式的性质……………………………………………………………………..…5 3 不等式的证明方法…………………………………………………………………….....6 3.1 比较法…………………………………………………………………………..……6 3.1.1 差值比较法……………………………………………………………...............6 3.1.2 商值比较法………………………………………………………………….......6 3.2 综合法………………………………………………………………………..............7 3.3 分析法………………………………………………………………………..............7 3.4 反证法………………………………………………………………………………..8 3.5 放缩法………………………………………………………………………………..8 3.6 数学归纳法…………………………………………………………………………..9 3.7 换元法………………………………………………………………………………..9 3.7.1 几何换元法……………………………………………………………………...9 3.7.2 利用对称性换元，化繁为简…………………………………………………..10 3.7.3 增量换元法……………………………………………………………………..10 3.7.4 三角换元法……………………………………………………………………..11 3.7.5 均值换元法……………………………………………………………………..11 3.7.6 向量换元法………………………………………………