Main Texts:

Horn and Johnson, Matrix Analysis Coddington and Levinson, Theory of Ordinary Differential Equations

Topics to be covered: Linear algebra (6-7 weeks): Review of undergraduate material from an abstract perspective, infinite dimensional vector spaces, norms, completeness, linear transformations and matrices, bilinear forms, finite dimensional spectral theory, normal forms, factorization theorems, resolvents, applications to optimization, least squares problems, numerical issues. ODE (4-5 weeks): existence and uniqueness results, linear systems, numerical approximations.