**Course Details:**

Time: MWF 9:55am-10:45am

Room: Van Vleck B219

Office hours: MWF 11am-12pm (VV505)

Instructor: Saverio Spagnolie

Office: Van Vleck 505

Course website: http://www.math.wisc.edu/~spagnolie/Courses/MATH705_2012/index.html

**Textbooks:**

You may be interested in visiting the following supplementary texts; the first four have been placed on reserve in the math library (Van Vleck B224):

- Acheson, Elementary Fluid Dynamics (Oxford Univ Press)
- Pozrikidis, An Introduction to Theoretical and Computational Fluid Dynamics (Oxford Univ Press)
- Batchelor, An Introduction to Fluid Dynamics (Cambridge Univ Press)
- Landau & Lifshitz, Fluid Mechanics [Vol 6] (Butterworth-Heinemann)
- Currie, Fundamental Mechanics of Fluids (CRC Press)
- Saffman, Vortex Dynamics (Cambridge)
- Childress, An Introduction to Theoretical Fluid Mechanics (Courant Lecture Notes)

**Course Content:**

This course will explore the dynamics of fluids from a rigorous mathematical perspective. Topics will include the kinematics of fluids, the Navier-Stokes equations, potential flows, vorticity dynamics, viscosity-dominated (Stokes) flows, lubrication theory, classical airfoil theory, boundary layers, and water waves. Discussions will take us from classical, centuries-old techniques to open questions of active research and just recently observed phenomena. Incoming students should have experience with partial differential equations and basic complex variables.

**Grading:**

The final grade will be set by scores on homework assignments (90%) and on a short project (10%).

**Homework/exam policy:**

Feel free to discuss the homework with each other, but you are required to write up and turn in your own solutions. The take-home exam should be completed on your own.

**Homework sets:**

Homework set #1 (Due 9/17/2012): HW #1

Homework set #2 (Due 10/01/2012): HW #2

Homework set #3 (Due 10/22/2012): HW #3

Homework set #4 (Due 11/12/2012): HW #4

Homework set #5 (Due 12/03/2012): HW #5

Homework set #6 (Due 12/19/2012): HW #6

**Miscellaneous:**

- National Committee for Fluid Mechanics Films
- Glorious Fluid Dynamics Blog
- Physics of Fluids
- Journal of Fluid Mechanics