论文标题
任意的差异和卷曲
The divergence and curl in arbitrary basis
论文作者
论文摘要
在这项工作中，使用差异几何形状的无坐标非刚性基准公式获得差异和卷曲算子。尽管作者试图尽可能地保持演示文稿的自言自语，但以前对差异几何语言的某些人可能会有所帮助。从这个意义上讲，这项工作的目的是为了较晚的本科生或初学者对数学物理感兴趣的研究生。为了说明开发，我们以图形方式介绍了Laplace操作员可分开的11个坐标系。我们详细介绍了圆柱和抛物面坐标系的基础和连接的开发。我们还在最大值和枫木中的[1]代码中提出了球形正顺序的基础，该基础是在其他感兴趣的情况下计算的工作模型。同样在[1]中给出了获得坐标表面的代码。
In this work, the divergence and curl operators are obtained using the coordinate free non rigid basis formulation of differential geometry. Although the authors have attempted to keep the presentation self-contained as much as possible, some previous exposure to the language of differential geometry may be helpful. In this sense the work is aimed to late undergraduate or beginners graduate students interested in mathematical physics. To illustrate the development, we graphically present the eleven coordinate systems in which the Laplace operator is separable. We detail the development of the basis and the connection for the cylindrical and paraboloidal coordinate systems. We also present in [1] codes both in Maxima and Maple for the spherical orthonormal basis, which serves as a working model for calculations in other situations of interest. Also in [1] the codes to obtain the coordinate surfaces are given.
