Functions and Analysis

   

Vector Differential Calculus

Authors: Eckhard Hitzer

This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships, which are necessary for vector differential calculus. Then differentiation by vectors is introduced and a host of major vector differential and vector derivative relationships is proven explicitly in a very elementary step by step approach. The paper is thus intended to serve as reference material, giving details, which are usually skipped in more advanced discussions of the subject matter. Keywords: Geometric Calculus, Geometric Algebra, Clifford Algebra, Vector Derivative, Vector Differential Calculus

Comments: 17 Pages. Mem. Fac. Eng. Fukui Univ. 50(1), pp. 109-125 (2002).

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[v1] 2013-06-17 04:00:42

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