What are the mathematical prerequisites of these books? In particular, what are the mathematical prerequisites of volume I?
For volume 1, you should be ok with multivariable calc and differential equations, plus a bit of linear algebra (eigenvalues and stuff). They have pretty high expectations as far as computational calculus skills go, especially to solve the problems. It probably helps to be familiar with the calculus of variations too, as it's not explained very well as far as I remember.
The mathematical requirements aren't that high: comfort with partial differentiation, vector calculus, ODEs, and matrices. But this shouldn't be your first exposure to most of the concepts, e.g. Lagrangian and Hamiltonian dynamics. Try Fowles or Symon.