Intro to differential forms (part 1)
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users point people to it when they want a visual intuition for 1-forms, dual vectors and differential forms.
Recommended by 2 people across 2 different months, 2014 to 2017.
What it is
The first part of David Metzler's video series introducing differential forms at the level of an intro multivariable calculus course. It motivates why vector fields may not be the best tool in some situations and sets up a visual, geometric way of thinking about forms.
What people said
Recommends James S. Cook · 2014-12 · Mathematics Stack Exchange · on “How to visualize $1$-forms and $p$-forms?”
You need to watch the video series on visualizing forms if you haven't already. Let's see, by David Metzler [this video]
Recommends got trolled too much this week · 2016-01 · Mathematics Stack Exchange · on “What is the intuition behind "dual vectors" in the context of tensor analysis?”
No time to write a full answer, but I suggest reading P. Szekeres's book. The part on tensors explains the various definitions and how they relate to each other [something that most physics books don't do]. It also covers visualizing dual vector spaces as stacks (which is based on Misner/Thorne/Wheeler), something that most linear algebra books don't do. For the latter you could also look at [this video] which is a bit long for my taste though.
Cites YoTengoUnLCD · 2017-02 · Mathematics Stack Exchange · on “What exactly is meant by "differential forms carry their own scale"?”
I've been watching this series: Intro to differential forms [this video] , where the author says every now and then something like "differential forms carry their own scale", "I can eyeball a path integral with differential forms, but not with a gradient picture, as I need a scale for the latter". Can someone explain or justify these statements? And also perhaps explain the idea of seeing differential forms (or perhaps just the exterior derivative of a 0-form $f$) as 'level sets' (of $f$)?