Mathematics 228: Mathematical Fluid Dynamics (Spring 2003)
Instructor
Linda Smolka
Description
This course is designed to give an overview of fluid dynamics from a mathematical
viewpoint, and to
introduce the student to areas of active research in fluid dynamics.
This course is aimed at first
year mathematics graduate students, although students in related fields
are encouraged to participate.
We will begin by deriving the governing partial differential equations
for a flowing continuum and discuss the
associated boundary conditions. After examining several exact solutions
for steady and unsteady laminar flows,
we will discuss two classic problems in fluid mechanics: Stokes flow
past a sphere and Prandtl's boundary layer
solution. We will also discuss problems related to hydrodynamic stability,
and if time permits, discuss the
dynamics of complex fluids (i.e., fluids composed of macromolecules,
such as polymers).
Requirements
Homework assignments will be due roughly every 1-1.5 weeks.
Prerequisites
A working knowledge
of complex variables (especially conformal mapping), ODEs, and a basic
knowledge of PDEs.
Text
To be announced.
Course Website
For more information see http://www.math.duke.edu/~smolka/fluids
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Last modified: 24 October 2002