Here are some notes on a A Crash Course in Geometric Algebra and Geometric Calculus. They are meant to be a swift and SUPERFICIAL introduction to the topic. The proofs, most examples, and many details are left out in favor of brevity. There are also many important topics that are not covered here. The reader who wishes to find useful ideas that are left out can quickly discover them in Macdonald’s A Survey of Geometric Algebra and Geometric Calculus. The emphasis here is on material which can be thought of as a natural outgrowth of multivariable calculus and linear algebra.
My hope is to eventually offer a much more complete set of notes in book form; the offering here is meant to be a preliminary to the later book.
Both the notes offered here and the later projected book depend on being able to construct such things as k-vectors, the wedge product, and the geometric product. For those who might be interested in the gory mathematical details of such a construction, I offer the pdf file Elementary Constructions of the Wedge and Geometric Products. This covers much of the material of the Monthly article The Wedge Product and Analytic Geometry but is more detailed and extends to constructions of the geometric product. A much briefer construction of the geometric product alone is to be found at Alan Macdonald’s website.