Hate to tell you this, but most of those topics aren't part of advanced calculus. That contains partial derivatives and multiple inegrals, the Jacobian, the implicit function theorem and maybe a deeper look at series. You might encounter the binomial expansion there but you'ld be more likely to spend time with Taylor series and different kinds of convergence. Likewise integrals, and uniform convergence. when I did it long ago it was full of epsilon and delta proofs (Weierstrasse's theory of continuity).
Several of the things you mentioned, like linear algebra, are subjects in their own right.