Introductory book on Tensor Product ,Exterior Product, and Vector Field

Question

I am studying linear algebra and facing difficulty in understanding Tensor Product ,Exterior Product, Vector Field .

My teacher says , Vector field can only be fully understood if we start from manifolds and tangent space . But he does not want to teach in that way because it is a physics Masters course . But I can't understand anything .

Can anyone suggest good book on this topics , understanding my problem?

Answer 1

Last year I bought "Introduction to Smooth Manifolds" of John M. Lee and I always use it to understand basic notions as those you ask. Best investment I've done, you'll keep it for years. Of course, if you cant spend this money, every good mathematical library should have it or you can easily find a pdf version on the internet.