Which multivariable calculus books are heavily oriented at physics?

Kline's Calculus, which someone else recommended doesn't cover multi-variable calculus at all, so that's definitely not what you want.

Mathew's Vector Calculus is a thin book that covers the basics quite well, and includes some material on suffix notation many texts omit. It's probably what you're looking for.

Marsden and Tromba's Vector Calculus is a standard text, with a reputation of being more difficult. It's thorough.

Lang's Calculus of Several Variables is nice if you're more mathematically oriented.

Antonio Galbis's Vector Analysis versus Vector Calculus is an interesting book if you want a book that goes more in depth into how things work.

Schey's Div, Grad, Curl and all that is a classic text explaining the ideas intuitively from a more physical perspective.

EDIT: And I just found another one that looks promising, a textbook which specifically emphasizes applications. Damiano and Freije's Multivariable Calculus. It's not too thick, and the writing looks relatively rigorous.It's expensive, but there are a number of reasonably priced used copies available on amazon.

I'm a fan of Hubbard's Vector Calculus, Linear Algebra, and Differential Forms. It's used in the freshman honors calculus class at Cornell. It emphasizes theory and gives proofs of everything, with the harder proofs relegated to an appendix in the back. It also shows how differential forms are connected to the usual div, grad, and curl using electrodynamics.

Although you may be looking for something "quick and dirty" in order to get to the physics faster, I'm a fan of the more theoretical, proof-based approach, which Hubbard's book emphasizes. If you just want the formulas, this is not the right book for you.