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Models in Applied Mathematics

ESAM C-21-2
Winter 1997

Hermann Riecke

Time and Place: TuTh 10:30-12:00 in Tech 1384

In this class an introduction will be given into two areas of science/engineering in which partial differential equations play a central role: fluid mechanics, electromagnetism.
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.
electro/magneto statics, vector potential, Coulomb's law, Biot-Savart law, derivation of Maxwell's equations, waves.
death and birth processes, queues, Monte Carlo method.

Recommended books:
C.C. Lin and L.A. Segel, Mathematics applied to deterministic problems in the natural sciences
L.A. Segel, Mathematics applied to continuum mechanics.

Note: the material of C-21-1 is useful but not required for C-21-2. Do you have any questions?
Phone: 491-8316, e-mail:

Homework Assignments: HW 1 HW 2 HW 3 HW 4 HW 5

Hermann Riecke
Mon Jan 13 19:05:31 CST 1997