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

Homework Assignment 1
Homework Assignment 2
Homework Assignment 3
Homework Assignment 4