Water waves are notoriously difficult to predict and manage mathematically. You can see a nice animation of the 'shallow-water equations' in MathWorld in a simple case. Here is the take of the National Oceanic and Atmospheric Administration on tsunamis with lots more information, including a short Quick-Time Video with realistic coastlines. The mathematics in here is called Partial Differential Equations (PDE). For almost all practical problems, you can only get approximate solutions - the keyword here is Numerical Mathematics. We will hear more about this in Chapter 5. PDE and Numerical Mathematics are studied in graduate-level math courses, but they all rely heavily on Calculus and derivatives for approximation.
A good description of the path of the tsunami of Dec 25, 2004 is on BBC Online.