Teaching myself multivariable calculus I want to learn multivariable calculus and I need a book suitable for self-study. 
I looked around on Amazon and found two books that seem to contain the right material:
Clark Bray: Multivariable Calculus
and
Larson/Edwards: Multivariable Calculus
Unfortunately, the first book is described as targeted at engineering majors (by the author himself on his website). And the second book seems to be too colorful and fancy so that I suspect it's also for engineering majors. 
I major in pure maths. 

Can I (a maths major) use either of these books (for engineering) to learn multivariable calculus? 
And if not, which multivariable calculus book is suitable for a maths
  major?

I am looking for an undergraduate low-level text with lots of exercises and  solutions. I want to practice the material as well as study proofs.
Edit
Why I am worried that these books might be no good to me: 
One thing is that since they seem to be written for engineers I am worried that there are no or only few proofs. The other thing that I'm worried about is that they don't cover the same scope of material like a book targeted at maths majors. 
Edit 2
After some more searching I found
Edwards: Advanced Calculus of several variables 
It looks good topic-wise but its title suggests that it's advanced and I only know first year real analysis in one variable. This book contains a chapter about differential forms (isn't that rather advanced?) Also, it does have exercises but no solutions. 
I am worried that this book is too advanced for me. 

Does anyone have any experience with this book?

 A: I strongly recommend the book "Multivariable Mathematics" by our very own Ted Shifrin.
In terms of difficulty, it is suitable, in my opinion, as a first "proof based" math course.  He does include the proofs of almost all of the important theorems in the text.
The book treats the needed linear (and multilinear!) algebra as needed for the development of multivariable calculus in the proper context, as well as an introduction to some topological ideas like compactness.  A wide range of very nice problems, and beautiful exposition.
You will also learn the calculus of differential forms in a particularly down to Earth way.
I think this is exactly what you are looking for.
A: Spivak "Calculus on Manifolds" is a favorite of mine. Do not be put off by the word "manifold"- they don't enter the picture till the last chapter. The presentation of Spivak is pretty elegant.
You can also have a look at Apostol's real analysis book. This book contains a lot of real analysis, and a few chapters on multivariable calculus. I personally find the treatment a bit less elegant than Spivak, but this book gives you a lot of examples.
(Also you might get copies of these books on the internet for free- but do not quote me on that ;-) )
