Collisionless modes of a trapped Bose gas

We calculate the excitation frequencies of the low-lying modes of a trapped Bose-condensed gas at nonzero temperatures. We include in our calculation the dynamics of the noncondensed cloud, and find agreement with experimental results if we assume that in the experiment both the in-phase and out-of-phase monopole modes are excited simultaneously. In order to explore whether this is indeed the correct explanation, we also calculate how strongly the modes couple to a perturbation of the external trapping potential.