[nicklaf]

Hubbard & Hubbard is a fantastic book; for the right audience, it may be all that is needed. I'd say that every mathematically minded engineer or physicist certainly should have it. It does a fantastic job of exposing the fundamental ideas of linear algebra and multivariable calculus--and in a way that doesn't require really any prerequisites beyond basic calculus. Reading this book is like being in a lecture with an experienced practitioner of both pure and applied mathematics simultaneously (well, this is actually true of Hubbard, but most texts are not written in a way that the author is so detailed and clear so as to seem present); the notes in the margins and the extensive, direct, and clear explanations are absolutely lovely.

That said, somebody interested in building a foundation for pure mathematics, and not so much motivated by the ability to solve problems outside of mathematics, would probably be better served by reading a standard text on real analysis.

On the other hand, I myself have turned to the notes in the margins of Hubbard & Hubbard, even when studying real analysis from the purest point-of-view, because the little tidbits are just so insightful.

Somebody who really took Hubbard & Hubbard seriously, though, could come away with a monster understanding of applied mathematics, while still having learned the craft in a way that is correct enough to lead to further study in pure mathematics as well. Nobody can really go wrong having this book on his or her shelf (although it is a bit expensive).