Geometrical vectors
by Gabriel Weinreich · first published 1998
3mentions
2recommended by
2HN commenters
2020–2022first – last mentioned
100% recommend
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Anyone interested in a visual exploration should checkout Geometrical Vectors by Gabriel Weinreich. https://www.maa.org/press/maa-reviews/geometrical-vectors
on “Why tensors? A beginner's perspective” ↗…study of smooth manifolds and differential forms. His exercises are approachable, and his book is the most expedient to the full theory of differential forms. As a quirky intuition pump, I recommend Geometrical Vectors by Gabriel Weinreich. The Fortney book mentioned in another comment is a nice, visual book, and there are other references in the replies to the comment I linked.
on “Differential Forms and Integration (2008) [pdf]” ↗The book Geometrical Vectors does exactly that. In fact, it considers the gradient vector to be a different kind of vector than a normal distance vector. If I have a vector between two points, and I compress space so that the points…
on “Intuitive Guide to Maxwell's Equations” ↗