多向量微分学
Multivector Differential Calculus
摘要：
泛几何微积分简化和统一了所有科学和工程以及技术应用的数学结构和符号。本文论述几何微积分中多向量微分学部分的基本原理。介绍了多向量微分，其次是多向量导数和多向量函数的伴随。明确地导出了多向量微分的基本规则，以及各种基本的多向量导数。最后讨论了向量变量函数与多向量变量函数之间的因式分解，并解释了单纯变量和导数的概念。一切都是在一个非常初级的一步一步的方法明确证明。因此，本文件旨在作为参考材料，提供一些细节，而这些细节在对该主题进行更深入的讨论时通常会被跳过。该材料的安排密切遵循{第2章的D。Hestenes，G. Sobczyk，Clifford Algebra to Geometric Calculus，Kluwer，Dordrecht，1999}.
英文摘要：
Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions. The basic rules of multivector differentiation are derived explicitly, as well as a variety of basic multivector derivatives. Finally factorization, which relates functions of vector variables and multivector variables is discussed, and the concepts of both simplicial variables and derivatives are explained. Everything is proven explicitly in a very elementary level step by step approach. The paper is thus intended to serve as reference material, providing a number of details, which are usually skipped in more advanced discussions of the subject matter. The arrangement of the material closely follows {chapter 2 of D. Hestenes, G. Sobczyk, Clifford Algebra to Geometric Calculus, Kluwer, Dordrecht, 1999}.
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