[wheelinsupial]

You can check the analysis courses offered where you took calc and linear algebra to see if you have sufficient prereqs.

Depending on the level of comfort or exposure you've previously had to proofs, it could be good to have a book covering introduction to proof handy. A book on counterexamples in analysis is also something I've seen recommended.

For proofs, something that covers direct proof, proof by contrapositive, proof by contradiction, and mathematical induction are good to be familiar with.

Delta-epsilon proofs are also good to have alternative or more accessible explanations to draw on.

If you're covering topics in multivariable calculus, then it might also be handy to cover some of the calculations from a calc 3/4 book to see implementations of it.