At the end of this course, the students will be able to 1. Use the concepts and methods of nonlinear dynamical systems for varying a bifurcation paramaters. 2. Reduce PDEs to ODEs using eigensystem methods. 3. Perform hydrodynamic stability analysis using method of normal modes. 4. Understand and perform formulations involving free and deformable surfaces and interfaces. 5. Understand basic hydrodynamic stability problems: Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau (Capillary) instabilities. 6. Undetstand Rayleigh-Benard thermal convection instability. 7. Undetstand shear flow instabilities.