No Title

**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.

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.

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: h-riecke@nwu.edu

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

* Hermann Riecke *

Mon Jan 13 19:05:31 CST 1997