“最值定理”的教学探究  

Teaching research on the maximum and minimum value theorem

作　　者：王志刚[1] 姚云飞[1] 

机构地区：[1]阜阳师范学院数学与金融学院,安徽阜阳236037

出　　处：《阜阳师范学院学报（自然科学版）》2014年第1期79-81,共3页Journal of Fuyang Normal University(Natural Science)

基　　金：国家特色专业建设项目(TS11496);安徽省级教学研究项目(2012jyxm344);阜阳师范学院教学研究项目(2013jyxm22;2010jyxm41)资助

摘　　要：最值定理是高等数学的重要定理之一,为物理、化学、生物、工程、经济管理和社会等领域的最优化问题奠定了理论基础。由于最值定理具有高度的抽象性,学生很难深刻理解,这对后继课程的学习和将来的研究非常不利。为了帮助学生理解最值定理,借助函数的图像直观感知最值定理;通过最值定理的理论证明完成感性认识到理性认识的升华;利用最值定理中的辩证法思想,培养学生的辩证唯物主义的思维方式。The maximum and minimum value theorem, which is one of the most important theorem in Advanced Mathematics, is theoretical foundation of the optimization theory in Physics, Chemistry, Biology, Engineering, Economic Management and Sociology. The maximum and minimum value theorem is so abstract that some students have difficulty understanding it, which is very disadvantageous for their future research and their learning of this subsequent courses. To help students better understand the maximum and minimum value theorem, the essence of this theorem was explained in class through geometric figures, algebraic proof and dialectics thoughts.

关 键 词：最值定理 有限覆盖定理 区间套定理 辩证法 

分 类 号：O172.1[理学—数学]