No Title

**Models in Applied Mathematics**

##### ESAM C-21-2

Hermann Riecke

Tu 10.00-11.00 (Searle 2378) and Th 10-12 (Tech 3829); discussion section Th 4-5 in A310

In this class an introduction will be given into three areas of science/engineering
in which partial differential equations play a central role:

fluid mechanics, electromagnetism, and elasticity.

The class is intended for senior students as well as
1st-year graduate students.
It will focus on two aspects:

i) the motivation and derivation of the fundamental
equations (Navier-Stokes, Maxwell, ...)

ii) the presentation of mathematical methods to solve the equations. This will be
done using concrete examples.

Topics to be discussed include:

Fluid Dynamics:

potential flow and conformal mapping, parallel flow and Orr-Sommerfeld equation,
a glimpse of turbulence, transition to complex behavior in simple model
(period-doubling cascade)

Electromagnetism:

electro/magneto statics, Coulomb's law,
Biot-Savart, vector potential, dielectric media, waves and diffraction

Elasticity:

stress and strain, generalized Hooke's law, Beltrami-Michel equations, elastic waves.

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

Syllabus
Homework Assignment 1

Homework Assignment 2

Homework Assignment 3

Homework Assignment 4

Books on reserve:

C.C. Lin and L.A. Segel, *Mathematics applied to deterministic
problems in the natural sciences*

L.A. Segel, *Mathematics applied to continuum mechanics*

G.K. Batchelor, * Introduction to Fluid Mechanics*

L.D. Landau and L. Lifshitz, * Fluid Mechanics*

* Hermann Riecke *

Wed Jan 3 17:38:50 CST 1996