I just enrolled for my PhD and after a few weeks I find that I am not very comfortable with n dimensional calculus and the related geometry behind it. Since its never late to learn anything in mathematics, I want to quickly revise the basics and the fundamental concepts so that I get a solid grasp of the subject. Can anyone suggest a way of achieving this ? Thanks.
I would suggest using the material here https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/index.htm
In addition I would buy a schaum's outline on multivariable calculus and work through as many problems as you can. I don't think there is a quick way to do this. I found a solid grasp of these ideas ideas essential for most of my PhD course work.