Advances in Applied Clifford Algebras

, Volume 12, Issue 2, pp 135–182 | Cite as

Multivector differential calculus



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 followschapter 2 of [3].


Product Rule Chain Rule Geometric Algebra Differential Calculus Geometric Multiplication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser-Verlag 2002

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringFukui UniversityFukuiJapan

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