Multivariable Calculus with Tensors I'm looking for a book at the undergraduate level on multivariable calculus (for a 2nd course of multivariable calculus) that introduces and makes use of tensors to describe higher order derivatives -- and maybe differential forms for integration. Does anyone know of a multivariable book that takes this tact?

Calculus on Manifolds - Spivak - A beautiful short little book. It carries you all the way to proving Stokes theorem.