关于多元微积分基本定理与Stokes公式的注记  

Remarks on Multiple Variable Calculus Fundamental Theorem and Stokes Formula

作　　者：罗玉文[1] 

机构地区：[1]重庆理工大学数学与统计学院,重庆400050

出　　处：《怀化学院学报》2010年第2期102-104,共3页Journal of Huaihua University

摘　　要：叙述了多元函数微积分的基本定理,说明了在平面上,微积分基本定理就是Green公式,在空间的情形,微积分基本定理就是Gauss公式,在曲面的情形,微积分基本定理就是通常的Stokes公式.并且,在引入外微分的概念后,这三个公式可以统一地用一个公式来表示,就是广义的Stokes公式.这样,为读者深入理解数学分析教材中的微积分基本定理提供帮助.In this paper, the author stated fundamental theorem of multiple variable calculus. On the plane, the fundamental theorem is Green formula; on the space, fundamental theorem of calculus is Gauss formula; and on surface, it is Stokes formula which we have studied. Furthermore, after the concept exterior differentiation be introduced, these three formulas can be expressed as one formula, that is, generalized Stokes formula. Then it will help readers to understand more deeply the fundamental theorem of calculus in textbook.

关 键 词：微积分基本定理 外微分 STOKES公式 

分 类 号：O186.15[理学—数学] O172.2[理学—基础数学]