This course will explore the dynamics of fluids from a mathematical perspective. Topics will include the kinematics of fluids, the Navier-Stokes equations, potential flows, vorticity dynamics, classical airfoil theory, boundary layers, water waves, and highly viscous flows relevant to physics at the micron scale. Discussions will take us from classical, centuries-old techniques to open questions of active research and just recently observed phenomena.
We will use as a springboard the following text: Acheson, D.J., Elementary Fluid Dynamics (Oxford University Press). Additional topics will be covered using supplemental materials.