中文摘要：

运筹学是许多工科学生尤其是金融工程系和企业管理专业学生非常重要的数学工具。尝试论述这样一种新的教学方案：在微积分教材函数极值部分突出运筹学中规划理论的基本内容——凸函数的一些性质。首先给出＂单谷函数＂的定义;然后举出一个实例说明仅有＂单谷函数＂的部分条件会产生一些不太好的函数特性,由此说明凸性这一良好的函数性质对求函数极值的帮助;最后给出一个用凸函数来描述的判定＂单谷函数＂的充分条件。

英文摘要：

Operations Research（O.R.） is an important mathematical tool of the students of engineering faculty.Particularly it is vital for the ones whose specialties are finance engineering and engineering management.Hence this paper tries to develop a seminal teaching scheme called highlighting some properties of convex functions involving the core concept and theory of linear and nonlinear programming in O.R.while the session of optimal points in calculus are taught.In this scheme a definition of ＂Unique valley function＂（U.V.F.） is presented first,and then an example exposed some ticklish phenomena because only a part of conditions of U.V.F.hold.By this way one can realize the effect of convexity for obtaining global or local optimal points of functions.Finally a identifying rule of a U.V.F.is proposed,which is described with the concept of convexity.