In addition, areas of science/engineering will be discussed in which probabilistic models and methods are used.
A major focus of the class will be the motivation and derivation of the fundamental equations (Navier-Stokes, Maxwell, ...). Therefore the experimental facts and mathematical assumptions used for the derivation will be stressed.
In addition, the mathematical methods required to solve the equations will be presented. This will be done using concrete examples.
For the probabilistic part the homework may include some programming (matlab, C, fortran).
Topics to be discussed include:
Fluid Dynamics: Conservation laws, derivation of Navier-Stokes, stress tensor, potential flow, parallel flows, hydrodynamic stability.
Electromagnetism:electro/magneto statics, vector potential, Coulomb's law, Biot-Savart law, derivation of Maxwell's equations, waves.
Probability:death and birth processes, queues, Monte Carlo method.
