# What is the best way to learn Differential forms?

I'm taking a Multivariable Calculus class and my teacher has just started Differential forms. It is not making a lot of sense, though. I have tried reading "Geometric Approach to Differential forms" by David Bachman and I have understood a bit, but I would like to get more feel of it.

I just want an introduction to the subject, not too much detail. I want to know if there are any online lectures I can see or a better book I can read from.

• Differential forms seemed like utter nonsense to me until I learned a little bit of topology. I think it would have been easier for me if someone told me that no, it's not supposed to really make sense, it's all in the physicist's nonrigorous style. – mathematician Sep 8 '15 at 12:57
• Welcome to Math.SE! Right now your question is rather broad: you are basically asking people to explain what differential forms are. Could you maybe narrow your question down somewhat more? – Hrodelbert Sep 8 '15 at 13:01
• I added a little more information. – Sahiba Arora Sep 11 '15 at 17:09
• I don't think this was an unreasonable question. Since no one else provided you a source, I will suggest you look at my course lectures on Multivariable Mathematics on YouTube. Differential forms start at Lecture 24 of the second semester. (At the very end you'll find a re-do of that lecture, as there was a technical glitch the first year.) – Ted Shifrin Sep 17 '15 at 20:10
• Thanks Ted Shifrin, I'll definitely go through the lectures. – Sahiba Arora Sep 18 '15 at 4:02

The advice given elsewhere for doing math homework would seem (to me) too apply here as well. .. Namely, step 1) write down the problem. Step 2) cry.

That being said, differential forms probably aren't any more difficult than any other topics in mathematics (with the possible exception of tensors; which as I recall are closely related)...

Spivak's Comprehensive introduction to differential geometry is one source I remember. ..

Or maybe try guilleman and pollack's differential topology, or even Marsden and tromba's vector calculus has a section on them, I think...

• The OP was doing a multivariable calculus course and you suggest Spivak? – user99914 Dec 16 '17 at 6:07
• I agree with @JohnMa Spivak is too elementary for the OP. – Landon Carter Dec 16 '17 at 13:51
• If anything it's too advanced. .. – Chris Custer Dec 16 '17 at 14:20