不等式的缩放是高等数学的灵魂  

Inequality zoom is the soul of higher mathematics

作　　者：刘照军[1] 岳超[1] 聂斌[1] 

机构地区：[1]泰山医学院信息工程学院,271016

出　　处：《中国科技信息》2009年第10期265-266,共2页China Science and Technology Information

摘　　要：通过具体例子说明不等式的放大与缩小在极限计算、泰勒公式应用、级数敛散的判定中的重要作用;阐明了高等数学与初等数学的本质区别;涵盖了高等数学学习方法的重要内容。对系统把握高数的抽象性与极强的逻辑性认识有一定帮助;特别是给出了在闭区间上具有单项二阶导数的函数平均值的限的估计新结论。Several specific examples are given to illustrate the important role of inequality zoom in limit calculation, the application of Taylor＇s formula, the judgement of series convergence. The essential difference between higher mathematics and elementary mathematics is explained, and important learning methods of higher mathematics is presented, which contribute to grasp systematic highly abstract and logical essence of higher mathematics. In particular, we get a new conclusion about limit estimate of functions mean value, functions possesses a single second derivative in the closed interval.

关 键 词：高等数学 不等式 放大与缩小 

分 类 号：O178[理学—数学]