Examine computational and variational methods for inverse problems governed by partial differential equations, including variational formulations, ill-posedness, regularization, adjoint methods for sensitivity analysis, variational discretization, and efficient large-scale optimization algorithms. Explore a brief introduction to the Bayesian formulation and relationship to the deterministic setting. Discuss examples drawn from different areas of science and engineering, including continuum fluid and solid mechanics, geophysics, and image processing. Computational Science, Engineering, and Mathematics 397 (Topic: Comput/Var Meths Inverse Probs) and 393P may not both be counted. Three lecture hours a week for one semester.