See if you can get your hands on Tom Apostol's Calculus Vol. 2. It's the textbook they use at Caltech. It covers Calculus III, Differential Equations, and Linear Algebra.
I'm taking calculus two right now and I will start cal III in December. I would like to jump ahead a bit and learn (or at least get familiar with) differential equations and linear algebra.
I would like books with an emphasis of proofs and theory, not application. Does anyone know of anything good?
Dennis Zill's ODE book is by far my favorite for undergraduate ODE. You can easily read it and understand how to solve the problems.
Stephen Leon's Linear Algebra with Applications is good as well. It isn't just computational work. It covers proofs as well.