From what it looks like, I would suggest reviewing Diff. Eqs. I know many mechanics courses also suggest Linear Algebra, but I didn't have it when I took mechanics and any linear algebra given in the class was stuff I had picked up pretty quick.

If you are looking for a deeper understanding of mechanics, some calculus of variations work wouldn't hurt...but I don't think it is absolutly necessary to pass this course.

you might be asked to solve a few ODE's. in my course, i recall having to solve a nonhomogeneous second order equation once during a homework assignment.

if you end up covering inertia tensors, you'll be building matrices with elements given by multidimensional integrals.

so you'll probably be good with the calc sequence and an introductory course to diff eq's.

Calculus of variations is a field of mathematics that deals with functionals, as opposed to ordinary calculus which deals with functions. Such functionals can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions: those making the functional attain a maximum or minimum value.

At my university we have 2 mechanics classes. An intermediate mechanics where we deal with rigid systems, keplers laws, periodic motion, chaos. Then we have a second "Advanced Dynamics" course that introduces Lagrangian/hamiltonian dynamics, calculus of variations, coupled pendulums, ect.
During intermediate mechanics all I needed was some calculus (about calc 2 level) and differential equations. We solved ALOT of differential equations. They were mostly homogeneous and second order.