Am I ready to learn tensor calculus? And what's a good book for it?

[Tosh5457]

Hi, the only thing I know is differential and integral calculus for functions with 1 variable and the basics of linear algebra (solving linear systems with matrices, determinants, etc...) . I'm currently learning differential and integral calculus for real functions with multiple real variables, and I can study more linear algebra if it's needed to learn tensor calculus.

Am I ready to learn tensor calculus knowing what I know? And can you recommend a good book for it? Thanks

 

[Rasalhague]

You'll want a good understanding of multivariable calculus, but that's no reason not to learn a bit about tensors, if you're curious and have a good introduction at a suitable level. I've found Bowen & Wang: Introduction to vectors and Tensors helpful. Many other texts assume knowledge of the material which they explain in the early chapters, the abstract algebra used to define concepts such as relation, function, group, algebraic field, vector space, dual space, inner product.

Vol 1: Linear and Multilinear Algebra
Vol 2: Vector and Tnsor Analysis