I'm trying to decide between a few books on multivariable ("advanced") calculus, with the following features:
- Should form a bridge between Spivak's Calculus (which I'll be finishing up in a bit, though not all chapters) and differential geometry (where I'm headed next)
- Should be suitable for self-study (so solutions or at least hints to problems would be nice)
- Should not be overly long or verbose (Hubbard & Hubbard, while well-regarded, is quite long).
I've narrowed it down to Edwards, Advanced Calculus: A differential forms approach and Callahan, Advanced Calculus: A geometric view. There's also the book by Bressoud, Second Year Calculus. Any recommendations between these three, or perhaps something else altogether? I'm not interested in "standard" books on multivariable calculus because these don't usually have a differential-forms focus.
I'm not an undergrad but for the purposes of this question, assume my math is at around the junior/senior level (I'm comfortable with abstract vector spaces). I'm after intuition rather than rigor if one must choose between the two. But I would prefer to not have to choose.
Lots of diagrams are nice (+Callahan), a focus on differential forms is nice (+all three above), a modern treatment is nice (+Callahan, -Edwards, $\pm$ Bressoud), relative brevity is good (-Callahan, which is on the long side).
I did look at Spivak's Calculus on Manifolds but it seems a bit too terse. Munkres' Analysis on Manifolds doesn't have (official) solutions but otherwise seems excellent for my purposes - it was actually my first choice. The book by Walschap (Multivariable Calculus and Differential Geometry) satisfies my criteria for a bridge between calculus and differential geometry almost exactly but lacks solutions. I did work through the first chapter and quite enjoyed it, FWIW.
As for where I'm headed after the missing link above, Tu's book on manifolds seems appropriate.
(I hope you enjoyed my very minor LaTeX joke above and will pour forth with recommendations as a consequence.)
(Edit: I realize this sort of question is asked a lot, but I was hoping that there was enough unique here to justify a new question - moderators feel free to close if you think this is just more of the same.)