Potential flows around bodies: panel singularities methods and conformal mapping methods. Finite-difference and spectral methods for Poisson equations: numerical inversion of matrices, and potential flows in or around irregular domains. Consistency, stability, and convergence of numerical methods: linear stability analysis. Numerical methods for diffusion equations and methods for ordinary differential equations. One-dimensional Burger's equation and nonlinear problems, Newton iteration, error analysis. Numerical methods for stream function vorticity equations: flows in or around irregular domains. Discussions of current research in computational fluid dynamics. Four exercise projects and one examination project will be assigned to each student. Prerequisite: Computer Programming.