You can't have too much math in this business, so you need to balance your depth of understanding to the desire to get up and running quickly.
I agree with the commenters about Lagrange multipliers. You also, at a minimum, need enough calculus to fake your way through a Newton-Raphson optimization argument.
If you want to understand the theory behind kernel operators, their eigenvalue decompositions, and the Riesz Representation theorem, then you need to delve into functional analysis -- this is basically linear algebra for infinite dimensional vector spaces with convergence thrown in. But you can practise machine learning without knowing all of that theory.
Bear in mind that it's called machine learning (as distinct from human learning), so it's probably more important to understand the algorithms that compute the answer rather than the mathematical theory, which only indicates the existence of an answer.
TL:DR Ignore the math; take the machine learning course; and whenever you come across something you don't understand, do the mathematical backfill. What math you need will depend on how the ML course is taught. A lot of those guys hate calculus and avoid it where possible.