How big of a field is Differential Forms?

pantheid · Jan 26, 2015

I have been reading a lot about Differential Forms lately because its so sexy. I have a pretty good grasp of how wedge product, hodge star, and differential operator "d" work, and their application to physics (it took me some time to see how d*F=J). I want to continue reading about it because I'm sure there more to it than a 30 page article and a wikipedia page, but I don't quite see where the more advanced materials are.

mfb · Jan 27, 2015

3.7 million hits in Google Scholar should be more material than you can ever read.

homeomorphic · Feb 1, 2015

It's not really a "field". There's a book called A Geometrical Approach to Differential Forms, another book by Harley Flanders, and lots of books cover that material under the heading of differential geometry or other subjects. V.I. Arnold's Mathematical Methods of classical mechanics gives one of the best descriptions I have seen.

bolbteppa · Feb 2, 2015

Hopefully it was this article

http://em.groups.et.byu.net/pdfs/publications/formsj.pdf

There are these 3 recent ones

https://www.amazon.com/Exterior-Analysis-Using-Applications-Differential/dp/0124159028/
https://www.amazon.com/Differential-Forms-Geometry-General-Relativity/dp/1466510005
https://www.amazon.com/Differential-Forms-Second-Theory-Practice/dp/0123944031/

that I wish were out when I first learned about forms.

HallsofIvy · Feb 2, 2015

I would say that "differential forms" is a subfield of "differential geometry". If you think "differential forms" is sexy, take a look at "differential geometry"!

Brian T · Feb 5, 2015

Differential forms is key in understanding and depicting General Relativity

mathwonk · Feb 5, 2015

henri carton is one of my favorite authors and he has a book on this topic:

https://www.amazon.com/Differential-Forms-Dover-Books-Mathematics/dp/0486450104

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How big of a field is Differential Forms?

pantheid

mfb

Staff: Mentor

homeomorphic

bolbteppa

HallsofIvy

Brian T

mathwonk