Fluid mechanics reaches from practical engineering problems
to difficult mathematical questions. Mathematics is involved in
formulating basic principles, modeling and
predicting observed phenomena, and designing
reliable numerical methods. No course can cover all the aspects
of this subject. This course will include a basic
treatment of the theoretical foundations of fluid mechanics,
and introductions to several topics, with emphasis on the incompressible
case (liquids, or gases at low speeds). Basic topics will include
(at least) the formulation and significance of the Euler and Navier-Stokes
equations for flow without or with viscosity; stress; vorticity; conservation
of circulation etc. in inviscid flow; potential flow and its relation to
Laplace's equation; boundary layers and the Prandtl equations;
and flow instabilities. Further topics may
depend on time and the interest of those enrolled.
Students should have some familiarity with partial differential
equations at either undergraduate or graduate level, a working
(not just passive) knowledge of vector calculus, and
the mathematical maturity of a graduating math major. Students
who are unsure whether their background is adequate are welcome to
consult the instructor, Tom Beale, beale@math.duke.edu.
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