ELEC 242: Fundamentals of Electrical Engineering II
Formulation and solution of equations describing electric circuits and electromechanical systems. Behavior of dynamic systems in the time and frequency domains. Basic electronic devices and circuits, including diodes, transistors, optoelectronics, gates, and amplifiers. Introduction to feedback control and digital systems. Students must register for both ELEC 242 and ELEC 244.

ELEC 302: Introduction to Systems
In many applications one is faced with the task of simulating or controlling complex dynamical systems. Such applications include for instance, weather prediction, air quality management, VLSI chip design, molecular dynamics, active noise reduction, chemical reactors, etc. In all these cases complexity manifests itself as the number of first order differential equations which arise. For the above examples, depending on the level of modeling detail required, complexity may range anywhere from a few thousand to a few million first order equations, and above. Simulating (controlling) systems of such complexity becomes a challenging problem, irrespective of the computational resources available. In this course we will set the foundations for model of linear systems. For this, state space representation will be introduced and analyzed. One of the main conclusions will be that certain appropriately defined singular values will provide the trade-off between accuracy and complexity of these dynamical systems.

ELEC 501/CAAM 651: Data-Driven Approximation of Dynamical Systems
Model reduction seeks to replace a large-scale system described in terms of differential or difference equations by a system of much lower dimension that has nearly the same response characteristics. Model (order) reduction (MOR) is commonly used in the simulation and control of complex physical process. The systems that inevitably arise in such cases are often too complex to meet the expediency requirements of interactive design, optimization, or real time control. MOR has been advised as a means to reduce the dimensionality of these complex systems to a level that is amendable to such requirements. The ensuing methods have been an indispensable tool for speeding up the simulations arising in various engineering applications involving large-scale dynamical systems. In this course we will develop the underlying approximation theory paying particular attention to its data-driven aspects.