Clifford Algebra to Geometric Calculus
A Unified Language for Mathematics and Physics
by David Hestenes, Garret Sobczyk · first published 1984
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…but given that @eigenspace is a physicist, what you are looking for (notations used, etc) is possibly here: http://geocalc.clas.asu.edu/html/Evolution.html#References under "Recent Books". Notably "Clifford Algebra to Geometric Calculus" and "New Foundations for Classical Mechanics" by Hestenes. PD: if you ever attempt to read any of those two, I'd advise to go to the latest (corrected) reprint.
on “Let's remove Quaternions from every 3D Engine” ↗…optimization on matrix manifolds) 4 on CS (highlight: CLRS’s intro to algorithms) 10 on calculus/geometry/topology/algebra (highlights: Bachman’s geometric approach to differential forms, Hestenes&Sobzyk's Clifford algebra to geometric calculus) 8 on fiction writing (highlight: Bickham’s Scene & Structure) And Rosenberg‘s Nonviolent Communication (not a textbook, but still a highlight worth mentioning). It amounts to between 3 and 4 per year.…
on “Ask HN: What is the best money you have spent on professional development?” ↗…revealing the relationship between electric and magnetic fields. I agree with the article that whatever its absolute merits, it would be a good way to teach new physicists. I have already ordered my copy of "Clifford Algebra to Geometric Calculus". Whether it is actually more practical to do work in General Relativity or Quantum Mechanics, or indeed Quantum Field Theory etc., I'll have to leave for the experts in those fields. From an outsider's…
on “Bret Victor's Bookshelf” ↗…not too much else pitched at a similar audience. MacDonald also has a book [Vector and Geometric Calculus][vagc] which I suspect will be substantially easier to work through than Hestenes and Sobczyk’s [Clifford Algebra to Geometric Calculus][cagc]. (I haven’t looked at either of MacDonald’s books) If you’re interested in geometric modeling for robotics, computer graphics, computer vision, or similar, check out [these papers][invkinematics]…
on “Clifford Algebra: A visual introduction (2014)” ↗