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