本人声明:该毕业设计是本人指导学生完成的研究成果,已经审阅过毕业设计的全部内容,保证题目、关键词、摘要部分中英文内容的一致性和准确性,并通过一定检测手段保证毕业设计未发现违背学术道德诚信的不端行为。 指导教师签名: 年月日不等式证明的若干种方法	高银梅 (集宁师范学院 数学系 数学与应用数学 2009级)	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、综合法、分析法、换元法、增量代换法、反证法、放缩发、构造法、数学归纳法、判别式法等等。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:柯西不等式、詹森不等式、施瓦茨不等式、赫尔德不等式等等。从而使不等式的证明方法更加完善,有利于我们进一步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,证明方法,常用,特殊 Abstract: both in elementary mathematics and higher mathematics, the inequality is very important content. Inequality and the proof is an important part of knowledge. In this article, I summarized some mathematical proof of the method of inequality. Inequality in elementary mathematics analyst is often used with comparison method, synthesis, analysis, change element method, incremental substitution method, the reduction to absurdity, zooming, construction method, mathematical induction, discriminant method and so on. Inequality in higher mathematics analyst often use of mean value theorem, Taylor formula, Lagrange function, and some well-known inequalities, such as cauchy inequality, Jensen's inequality, inequality Schwartz, held, and so on. So that the inequality proof method more perfect, good for our further discussion and study of inequality proof. By studying these proofs, can help us to solve some practical problems, to cultivate logical reasoning ability and abstract thinking ability and the students to form good learning habits of thinking, good at thinking. Keywords: inequality, the proof method, commonly used, special