I second the recommendation to at least flip through <i>Gravitation</i>.  It has an intimidating size, but easygoing manner.  I had a lot of difficulty with Spivak's <i>Calculus on Manifolds</i> (which has essentially no physical intuition outside the Archimedes exercise at the end), but I think I was uncomfortable with the abstract notions of tensor product and dual vector space at the time I was learning from it.

You might try [Sternberg's Advanced Calculus][1] (available on line), especially chapters 11 and 13.

  [1]: http://www.math.harvard.edu/~shlomo/