Reddit reviews Differential Forms: A Complement to Vector Calculus

For an elementary account, there is a book by Weintraub called Differential Forms, which is very accessible. It is explicitly written as a "complement to vector calculus".

For a more advanced treatment take a look at Arnold's Mathematical Methods of Classical Mechanics. There is a standalone chapter on differential forms which is extremely well-written and well-motivated (as is the rest of the book, for that matter).

This was the book I used when I took Advanced Calculus II:

http://www.amazon.com/Differential-Forms-Complement-Vector-Calculus/dp/0127425101

It was really really straight-forward and really funny at times. I think it's a good book and has decent enough explanations with a good amount of exercises.

> http://www.amazon.com/Differential-Forms-Complement-Vector-Calculus/dp/0127425101

I'm currently working through this, and enjoy it a lot!

I learned from Differential Forms: A Complement to Vector Calculus and Advanced Calculus: A Differential Forms Approach. In first book many of the exercises seem tedious, but you should do them anyway.