I've tried learning basic tensor calculus (transformation law, inner & outer products, adding , etc..) and I could 'work' with the math with no problem, but sometimes I couldn't quite understand what I'm doing, is there a book that completely explains what is exactly happening and that has both mathematical and intuitive 'approaches'?
Is there a book that:
• Goes mathematically in depth with tensors (with a background of multivariable calculus and differential equations)
• Explains where everything comes from ( intuitive reasoning or mathematical proofs)
• Explains how they are used and why
In short, is there a book that gives you complete intuition about them?