利用斯托克斯公式求第二型曲线积分的一点思考

Some Thoughts on Evaluating Second-Type Curve Integrals by Stokes’ Formula

摘要: 本文探讨了第二型曲线积分的求解方法，重点阐述了如何利用斯托克斯公式求解第二型曲线积分，文中结合例题展开讲解，针对以有向闭曲线为边界所张成的不同有向曲面，详细分析利用斯托克斯公式进行求解的过程，并总结如何选择有向曲面能使求解更为简便。

Abstract: This paper investigates the solution methods for line integrals of the second kind, with emphasis on evaluating such integrals by means of Stokes’ formula. Explanations are illustrated with typical examples. For different oriented surfaces bounded by an oriented closed curve, the solution procedures using Stokes’ formula are analyzed in detail. Moreover, the paper summarizes how to select a proper oriented surface to simplify the calculation.