Most vector/tensor analysis textbooks use index notation in their formulas extensively. The fact that I constantly have to keep track of the indexes as well as the meaning of the variable gives me three problems:
Although understanding the equations and their derivations (I can actually derive them), I am usually distracted from interpreting their geometrical/physical meanings (because I have to focus on keeping track of the indexes).
Sometimes, a variable has several indexes with it. For example: $$x^{ij}_k$$ and in cases like this, although understanding the meaning of this variable and how it changes as i, j, k vary between 1, 2, 3, keeping in mind the meaning is very hard for me and I constantly have to go back to its original definition to remind myself.
As a result from 1 and 2, although understanding separate parts of a chapter, I have a hard time seeing how different parts connect with one another (the big picture). This is because my main focus has been dealing with notations.
I feel like there is something wrong with the way I am dealing with index notation. What I mean is that the way I am working with them is not wrong, but perhaps that's not the most efficient/effective way.
My question is: Could you give me your advice/tips on dealing with index notation? Thank you.
The book "Concrete Mathematics" by Donald Knuth, Oren Patashnik, and Ronald Grahamis is all you need.