外积与外微分运算及其应用

The Product and the Differential Operation and Its Application

简要介绍了微分几何的发展和外微分在微分流形中的重要性,着重讨论向量代数与外积运算的相关性,探讨向量分析与外微分的关系,并得到了多种常用运算公式的外微分表示,最后从外微分角度,对数学分析中四大基本公式(莱布尼兹公式、斯托克斯公式、格林公式、高斯公式)作了统一表述.

In this paper,the development of differential geometry and the differential in differential manifolds were briefly introduced,the importance and the vector algebra accumulate computation were discussed,the relevance vector analysis and outer differential relationship were also discussed,several common operational formulas of the differential said were obtained.Based on the outside differential angle,the mathematical analysis four basic formula（Leibnitz formula,stokes formula,green formula,gaussian formula） to have the unification expression were presented.