Differential forms and vector analysis

Question

where can I learn about differential forms, what they represent and how to integrate them.

PS: Where can I read about vectorial spaces and vectorial analysis, especially how to integrate.

I need these to understand my physics course, classical mechanics.

Answer 1

There are plenty of books about differential forms and each of us will have a personal favourite. If you are starting out, I would suggest maybe having a look at:

• Vector Analysis Versus Vector Calculus by Antonio Galbis
• Differential Forms:A Complement to Vector Calculus by Steven H. Weintraub
• Advanced Calculus: A Differential Forms Approach by Harold M. Edwards

Hopefully one of those will have what you need. I am sure there are also plenty of notes you could find online that cover similar material.

Answer 2

Try "Mathematical Physics" by Mary L. Boas. It is a very good textbook for learning things from the essential basics.