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## Main Question or Discussion Point

Hi. I am looking for a book about tensor analysis. I am aware that there have been some post about those books, but I wish to find a thin book rather than a tome but just good enough for physics, such as group theory, relativistic quantum mechanics, and quantum field theory.

I am reading

For example,

By the way, what would you do if the problems in some book are hard to solve? I have read

I am reading

*Mathematical Methods for Physicists*by Arfken, Weber, Harris. The content in the chapter of tensors is quite easy to understand, but when it comes to the exercises, I can only solve half of them. Besides, even looking at the solutions, I can not understand them.For example,

The solution is just a sentence thatIf ##T_{...i}## is a tensor of rank ##n##, show that ##\partial {T_{...i}} / \partial {x^j}## is a tensor of rank ##n+1##. (Cartesian coordinates).

I cannot understand the solution at all. Maybe the content of this chapter is not self-content?As the gradient transforms like a vector, it is clear that the gradient of a tensor field of rank ##n## is a tensor of rank ##n+1##.

By the way, what would you do if the problems in some book are hard to solve? I have read

*nonlinear optics*by Boyd and*quantum optics*by Scully. I find that I can handle the content of these two books, but I can not solve most of the problems. My tutor ask me to just read the books, and leave the problems aside. However I do not feel good enough if I cannot solve problems. Maybe I have some problems....