I am a physicist trying to learn vector calculus in a way that is a mixture of the way mathematicians learn it with the way that physicist learn it in order to be able to learn Differential Geometry the right way afterwards.
After asking myself what the geometrical meaning of the chain rule is, I came to the conclusion that I haven't got the right intuition to figure it out on my own.
So, I wanted to ask if anybody knows of a book on Vector Calculus that deals with the subject material in such a geometrically intuitive manner.
Note: I don't want a book that only explains things qualitatively. I want a book like, say Marsden and Tromba's, but with more emphasis on intuition.