格林定理的证明与分析

The Proofs and Analysis of the Green's Theorem

分析矢量场中的重要定理,电磁场理论的重要数学工具——格林定理。研究格林定理中的空间闭区域上具有一阶及二阶连续偏导数的函数。分析公式中函数的方向导数和拉普拉斯算子。利用高斯公式证明格林定理,利用格林公式和两类曲线积分之间的联系分析导出平面上的格林公式。

The Green＇s theorem is an important theorem and mathematical tool for the research on electromagnetism. This paper studies the function of the Green＇s Theorem with the first-order and second- order continuous partial derivative in the closed-range of space analyses the directional derivative and Laplace Operator in the formulas, justifies Green＇s Theorem with Gauss formula. Moreover, Green＇s formulas in the plane are derived based on the relation between the Green＇s Theorem and the eurvilinear integrals.