E.M.S. Hitzer

*Advances in Applied Clifford Algebras*
**12**(2) pp. 135-182 (2002).

**Abstract:**
Universal geometric calculus simplifies and unifes 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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