[cooper]

I used Fitzpatrick for Adv Calc and based on my experience it is probably better to do this before the Grad analysis course. You will still have to prove things rigorously which is important.

Given your background, you may find it extremely difficult in the grad course since they would assume you are familiar with the 'epsilon-delta' arguments from Fitzpatrick. Also, in Adv Calc, you will learn basic topological concepts on the real line, which you should understand before generalizing to more abstract setting as you would in the grad course. Plus, there will more likely be a higher standard in the grad course since most students have studied analysis at the undergrad level already, while Adv Calc is usually the first course in Analysis,

More importantly, the Adv Calc course will provide the rigor that you need from an analysis course. You will have to think logically and you will get good practice constructing proofs so I think it is sufficient for first year Econ. In first year econ, you may have to think about function spaces or measure theory concepts, but not at a very deep level, and if you do well with Fitzpatrick, you will have the tools to handle these more advanced concepts on your own.

After the first year, you may need to think about more advanced math courses depending on your interests, but you can worry about that when you get there. Also, from a point of view of risk, it is probably better to get in A in Adv Calc than a B or even a C in Analysis.