**Courses Taught in Recent Years**:
**AM125abc - Engineering Mathematical Principles.**
*9 units (3-0-6); first, second, third terms: Prerequisite: ACM 95/100 abc.* Topics include linear spaces, operators and matrices, integral equations, variational principles, ordinary and partial differential equations, stability, perturbation theory. Applications to problems in engineering and science are stressed.
**CDS 201 - Applied Operator Theory. **
*9 units (3-0-6); first term: Prerequisite: ACM 95/100 or equivalent.* Invariant subspaces, Jordan form, Cayley-Hamilton theorem, matrix exponential, singular value decomposition, some Banach and Hilbert spaces, operators, duals adjoints, induced norms, and spectral theory. Calculus in linear spaces, the inverse and implicit function theorems. Taught concurrently with AM125a.
**CDS 270 - Advanced Topics in Systems and Control - Sec. 3: Stochastic System Analysis and Bayesian Updating. **
*9 units (3-0-6); third term. *This course focuses on a probabilistic treatment of uncertainty in modeling a system's behavior and its excitation. We start by examining the foundations of probability as a multi-valued logic for plausible reasoning with incomplete information; this leads to a rigorous meaning for the probability of a model for a system. We then focus on new approximate analytical and stochastic simulation tools for robust system analysis and Bayesian system identification that have been developed over the last decade or two. The topics covered include: Bayesian updating of models of a system to predict its future behavior based on measured response, including new Markov Chain stochastic simulation techniques; Bayesian model class selection with a new information-theoretic interpretation that shows that it automatically gives a quantitative Ockham principle of model parsimony; recently-developed stochastic simulation techniques for evaluating the response of stochastic dynamic systems subject to stochastic excitations, especially computing small failure probabilities (i.e. probability of the system reaching some undesirable state); and Bayesian sequential estimation of system states and model parameters, generalizing the Kalman filter.
**Summer Lectures at Caltech on Stochastic System Analysis and Bayesian Updating** **(2005)**** **
This is a new course that the lecturers are jointly preparing that focuses on stochastic system analysis and Bayesian updating. We will discuss the interpretation of probability as logic for plausible reasoning with incomplete information; Bayesian updating of models of a system to predict its future behavior based on measured response, including new stochastic simulation techniques; model class selection with a new information-theoretic interpretation that shows that it gives a quantitative principle of model parsimony; recently-developed stochastic simulation techniques for evaluating the response of stochastic dynamical systems subject to stochastic excitations; Bayesian sequential estimation of system states and model parameters; and other topics. |