关于曲线和曲面积分的换元法  

On Change of Variables for the Curve Integral and the Surface Integral

作　　者：詹华税 ZHAN Huashui(School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China)

机构地区：[1]厦门理工学院应用数学学院,福建厦门361024

出　　处：《厦门理工学院学报》2020年第5期89-92,共4页Journal of Xiamen University of Technology

摘　　要：在归纳、总结坐标变换下相应积分换元法的基础上,应用一阶微分形式的不变性提出曲线积分的换元法,利用微分几何外微分的方法得到三重积分换元方法下的曲面积分换元法。研究结果表明,提出的换元法可有效解决坐标变换下的曲线和曲面积分问题,简化曲线和曲面积分的计算过程。Applying the invariance of the differential form of first order based on the integral change of variables in coordinate transformations,the change of variables formula for the curve integral is found,and using the exterior differential calculation of differential geometry,the change of variables formula for the surface integral obtained.These results show that by change of variables a different coordinate system can be applied which simplifies the calculating process of the curve integral and the surface integral.

关 键 词：曲线积分 曲面积分 换元法 外微分法 

分 类 号：O172.2[理学—数学] O186.12[理学—基础数学]