CAJ | 학술논문

本文介绍高等数学中的三个创新案例，即多元函数极值的一阶导数判别准则、多变元情形下的罗尔中值定理，以及一元函数罗尔中值定理的推广定理。它们贴近高等数学课程中经典的教学内容，同时是在经典内容基础上的创新。本文研究这三个创新案例的推广过程，揭示其中蕴涵的数学创新思维方法，探讨其中体现的教学价值。
본문개소고등수학중적삼개창신안례，즉다원함수겁치적일계도수판별준칙、다변원정형하적라이중치정리，이급일원함수라이중치정리적추엄정리。타문첩근고등수학과정중경전적교학내용，동시시재경전내용기출상적창신。본문연구저삼개창신안례적추엄과정，게시기중온함적수학창신사유방법，탐토기중체현적교학개치。
In this paper, we present three innovative examples in advanced mathematics, i.e., the first-order derivative criterion of extremum of function of several variables, Rolle's mean value theorem in several-variable case, and the generalization of Rolle's mean value theorem. They are very close to the classic contents of advanced mathematics. Meanwhile, they are innova-tions based on those classic contents. By analyzing the thinking process of the three theorems, we reveal the ideology and methodology of mathematical innovation and discuss their educa-tional value.