平面上封闭曲线下的曲线积分的一种解法  

The Solution of Curvilinear Integral under a Closed Curve in a Plane

作　　者：杨志叶 YANG Zhiye(Foundation Department,Liaoning Institute of Science and Technology,Benxi Liaoning 117000,China)

机构地区：[1]辽宁科技学院基础部,辽宁本溪117000

出　　处：《辽宁科技学院学报》2023年第4期17-18,共2页Journal of Liaoning Institute of Science and Technology

摘　　要：给出了这一类∮_(L)xdy-ydx/mx^(2)+y^(2)无重点分段光滑封闭曲线包围的区域含有奇点的曲线积分的一种解法,通过取具有充分小边长的正方形状的封闭曲线l包围奇点,基本思想是利用常数的微分为0,原因在于这个小正方形在坐标系中的表示,可以使一些自变量的微分为0,适用于满足“格林公式”的大部分含有奇点的封闭曲线下的曲线积分。This paper presents a solution of the line integral∮∮_(L)xdy-ydx/mx^(2)+y^(2)(m>0),where L is a piecewise smooth,simple closed curve that forms the boundary of a region D in the xy-plane and(0,0)∈D.By taking a closed curve of square shape with sufficient small side length to enclose the singular point,the basic idea is to use the differential of constant being 0.The reason is that the expression of this small square in the coordinate system can make the differential of some independent variables become 0.It is applicable to the curve integral under a large part of closed curves containing singular points that meet the"Green's formula".

关 键 词：格林公式 封闭曲线 奇点 曲线积分 

分 类 号：O13[理学—数学]