ABSTRACT
This chapter introduces geometric vector differential calculus. The fundamentals of vector differential calculus are treated as part of universal geometric calculus. Geometric calculus is seen to simplify and unify the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment reasonably self-contained, also the most important geometric algebra relationships are provided, which are necessary for vector differential calculus. After that 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. This chapter is thus intended to serve as reference material, giving details, which are usually skipped in more advanced discussions of the subject matter. [122 words]
