关于散度、旋度和梯度及有关定理的注记

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A Note on Divergence, Rotation and Gradient and Their Associated Theorems

1.
Institute of Mathematical Sciences, Academia Sinica, Wuhan;
2.
Department of Electrical Engineering and Computer Science, University of Michigan, USA

摘要: 本文是关于散度、旋度和梯度的统一定义的继续和在并矢与实复转化等方面的补充,目的在于推广外微分形式的一种表写及其应用.

Abstract: In this note, the essence and some supplements for the unified definition of divergence, rotation and gradient advanced by Tai have been presented based on the method of exterior differential form with an expression of vectors of tensors. The main purpose of this note is to introduce the useful expressions and their applications, and to simplify the proofs of many theorems in various field theories, and they are also important because of their utlity for establishing a wide class of principles.

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