Math 654: Introduction to Fluid Dynamics                Winter 2024
Instructor: Silas Alben, 4858 East Hall, tel. 734-647-5518,
email: alben at umich.edu (usually the best way to contact me).

Time and Location:  Mon. & Wed. 2:30 - 4, 4096 East Hall.
Office hours: Mon. & Tues. 11-12 or by appointment.

Course Description:
The course is a broad introduction to fluid dynamics. We'll use
classical applied mathematical tools to gain physical insight into
fluid phenomena. No knowledge of fluid mechanics is assumed,
but some upper-level undergraduate mathematics is
(see pre-reqs below).

Topics: Continua and conservation laws. Inviscid flow.
Irrotational flow. Vorticity. Complex variable methods. Water waves. Airfoil
theory and conformal transformations. Viscosity and the Navier-Stokes equations.
The limit of zero Reynolds number. Boundary layers. Flow instabilities. Possible special
topics: fluid-structure interactions and biological propulsion.

Pre-requisites: Vector calculus. Complex analysis and differential
equations at a senior undergraduate level (Math 450).
Elementary physics (mechanics). Please contact me if you are unsure
about the pre-requisites.

Grading: The grade will be based on homework assignments given
every ~3 weeks. Class attendance and participation will not be graded but is encouraged.

Required text:
Elementary Fluid Dynamics by D. J. Acheson, Oxford University Press, 1990.

Some other useful references: