微分学中的代数方法

Algebraic Methods for Differential Calculus

文章用代数的方法讨论了微分学中的某些问题(如曲线、曲面的切空间、极值、凸函数理论等),得到了许多有趣的命题;由于在微分学中引进了代数概念,使许多难于理解的概念和证明方法都变得简单。此外,导函数的连续性及导函效的代数结构也在文中进行了讨论,并得到了一些有趣的结果。

This paper introduces the algebraic method for discussing the problems in differential calculus, and puts forwards many interesting propositions. The introduction of the concepts in algebra makes simple many concepts and verifications which have been difficult. Furthermore. the continuiy and algebraic structure of derived functions are discussed, leading to some interesting achievements.