If the initial conditions are also prescribed exactly, then the entire future of the system is determined. They are now used in a huge variety of models and applications throughout science and technology. In practice even predicting the distribution is extremely difficult, as it is governed by a partial differential equation in many variables. The student should have had an introduction to differential equations and also computer programming. A student who is a declared Math major is entitled to use the Math Dept.'s computer facilities.
Final outcome is determined with the interested students on a case by case basis.
Although not required, can lead to a senior thesis project.