线面积分中的三大公式辨析  

Analysis of the Three Formulas in Line Surface Integration

作　　者：张锐 吴明永[2] ZHANG Rui;WU Mingyong(School of Information Engineering,Lanzhou City University,Lanzhou Gansu 730070;BaiLie School of Petroleum Engineering,Lanzhou City University,Lanzhou Gansu 730070)

机构地区：[1]兰州城市学院信息工程学院,甘肃兰州730070 [2]兰州城市学院培黎石油学院,甘肃兰州730070

出　　处：《甘肃高师学报》2025年第1期92-96,共5页Journal of Gansu Normal Colleges

摘　　要：文章结合梯度、散度、旋度的概念,对格林公式、高斯公式、斯托克斯公式之间的关系进行了深入分析,总结了三个公式的关系.高斯公式、斯托克斯公式都是格林公式的推广,格林公式有切向量和法向量两种形式,其切向量形式向空间推广就是斯托克斯公式,其法向量形式向空间推广就是高斯公式,三个公式反映的都是区域内部某种量的积分等于其边界上另一种量的积分.Based on the concepts of gradient,divergence and rotation,the paper deeply explores the relationship among Green formula,Gauss formula and Stokes formula.It is pointed out that Gauss formula and Stokes formula are both extensions of Green formula.Green formula has two forms:tangent vector and normal vector.When the form of tangent vector is extended to space,it is called Stokes formula,and when the form of normal vector is extended to space,it is called Gauss formula.All the three formulas reflect that the integration of a certain quantity inside a region is equal to the integration of another kind of quantity on its boundary.

关 键 词：格林公式 高斯公式 斯托克斯公式 辨析 

分 类 号：O172[理学—数学]