Advanced Multivariable Calculus, I
Math 324, Advanced Multivariable Calculus I, is at the same time the natural prosecution of the Calculus sequence, and the first in the Advanced Calculus sequence.
In this sense, it is based on the material covered in the 124-125-126 sequence (or 134-135-136), but it is more abstract in the material covered, with topics like vector fields and their integration. For a brief description of the course, and the prerequisites, see here.
The text is Calculus, by Stewart, seventh edition. You may use the paperback Multivariable
Calculus, by Stewart, which starts with chapter 10. We will cover (essentially) the final parts of chapters 14, 15, and then we will focus on chapter 16. Be sure to be confident on the topics in the first parts of chapters 14 and 15, and in chapter 12.
We will also use some notes on differential forms that you can find here, and some notes on Geometry vs Calculus that you can find here.