Vaughn Climenhaga

I spent summer 2005 working in the Applied Mathematics Department at the University of Waterloo under the supervision of Kevin Lamb, looking at a method for incorporating first-order nonlinearities of surface water waves into a linear model. I wrote up my findings, such as they were (and they are mostly a summary of research that other people have done) -- the resulting document ought to be accessible to anyone with a thorough grounding in undergraduate mathematics up to the junior or senior level.  So without further ado, here follow 73 pages of me going on about Hamiltonian mechanics, Lie transforms, and other exciting ways to spend your summer:

Hamiltonians and Surface Gravity Waves:  With an introduction to Birkhoff normal form