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Differential forms for scientists and engineers

机译:科学家和工程师的差异形式

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摘要

This paper is a review of a number of mathematical concepts from differential geometry and exterior calculus that are finding increasing application in the numerical solution of partial differential equations. The objective of the paper is to introduce the scientist/ engineer to some of these ideas via a number of concrete examples in 2, 3, and 4 dimensions. The goal is not to explain these ideas with mathematical precision but to present concrete examples and enable a physical intuition of these concepts for those who are not mathematicians. The objective of this paper is to provide enough context so that scientist/engineers can interpret, implement, and understand other works which use these elegant mathematical concepts.
机译:本文回顾了微分几何和外部演算中的许多数学概念,这些概念正越来越多地应用于偏微分方程的数值解中。本文的目的是通过2个,3个和4个维度的具体示例向科学家/工程师介绍其中的一些想法。目的不是要以数学精度来解释这些思想,而是要提供具体示例,并使那些不是数学家的人对这些概念有直观的认识。本文的目的是提供足够的上下文,以便科学家/工程师可以解释,实现和理解使用这些优雅数学概念的其他作品。

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