As an R user, I can tell R actually does not have any Numerical Analysis
capabilities "by itself". However, many well-known and well-tested Fortran
subroutines implementing numerical methods do have R interfaces. This
includes virtually everything one could expect from a numerical package,
including quadrature, minimization, interpolation, solution of initial- and
boundary-value problems, and more. Definitely way more than what a
statistician would ever need. "The R Journal" has plenty of articles about
that.
Apparently, what is missing is Maxima's symbolic computations (although I
wonder how a statistician could really need that as well.) In general, I
have serious doubts if R is still a "software environment for statistical
computing and graphics", as R webpage states. it seems to me more or less
similar to packages like Scilab, Octave, and others, except that the syntax
is not Matlab compatible.