tensor calculus for undergraduates ? (textbooks) What textbook would you suggest for undergraduates to learn about tensors?  I am looking for an introductory book about tensors and tensor calculus.
Thanks!
 A: There are a lot of good references discussing the topic in different ways. Let me list some of my favourites:

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*The Geometry of Physics - T. Frankel

*Geometry, Topology and Physics - M. Nakahara

*Analysis on Manifolds - J. Munkres

*Multilinear Algebra - W. Greub

*Linear Algebra via Exterior Products - S. Winitzki

*Advanced Linear Algebra - S. Roman
The first two books treat a large amount of subjects in mathematics, including tensor calculus, geometry etc. The aim is to provide a bridge between mathematics and physics. In Munkres's book, you will find a nice exposition about tensor products of vector spaces, which is used in the study of multivariate integrals. Greub's book is a more abstract account on the subject (and, in my opinion, more advanced), but a very nice reference too. Maybe Winitzki's book is more appropriate for you, since the book is a linear algebra-type of book, so it has proofs for theorems and some nice tools for direct applications too. Roman's book also treats the case of tensor products of vector spaces.
