I am looking for a very rigorous calculus book that covers the topics of operators in curvilinear coordinates and an introduction to the tensor calculus.
I've already read Cartan's book about calculus on Banach spaces but it not cover nothing about change of coordinates, so I'll be grateful if somebody knows some rigorous texts.
I'll use it for qualitative theory of diffetential equations and some multivariate variational calculus.
Thank you.