EE 501 Principle of Mathematical Analysis

Vector spaces, function spaces, linear transformations, convex and concave functions, metric spaces, convergent sequences, compactness; Differential calculus on Rn; Continuity and limits, sequences of functions, Gateaux and Frechet derivatives, Mean-value theorem, Taylor’s theorem, inverse function theorem, implicit function theorem, manifolds; Integration: Riemann Integration, intervals, measure, integrals over Rn

EE 502 Linear System Theory

Linear spaces, normed linear spaces, metric spaces, Hilbert spaces. Matrix representation of Linear Transformations, change of basis. Fundamental theorem of differential equations. Dynamical systems. State transition matrix, impulse response matrix. Variational equation. Dynamic interpretation of eigenvalue-eigenvectors. Minimal polynomials, function of a matrix, bounded-input bounded-output stability, equilibrium points, stability in the sense of Liapunov. Algebraic equivalence, controllability,observability, minimal realization.

EE 556 Nonlinear System Theory

Nonlinear differential equations, Induced norms and matrix measures; Second order systems, Linearization methods; Approximate analysis methods, Describing functions,Singular perturbations; Lyapunov stability, the Lur’e problem ; Input-Output stability,Linear time-invariant feedback systems; Differential geometric methods, Frobenius Theorem,reachability and observability, feedback linearization, stabilization of linearizable systems.

EE 543 Artificial Neural Systems

Biological neuron, McCulloch-Pitts neuron model, feedforward network, feedback network,supervised and unsupervised learning: Hebbian learning rule, perceptron learning rule, delta learning rule; Single-layer perceptron classifier, linear machine and minimum distance classification; Multilayer feedforward networks, error back-propagation training; Single-layer feedback networks; Associative memories, cellular neural networks; Matching and Self-Organizing networks, character recognizing networks, linear programming modeling network, expert systems for medical diagnosis.

EE 201 Circuit Analysis I

Lumped circuits: Kirchoff’s laws, circuit graphs, circuit equations, linear and nonlinear resistive circuits, first and second order dynamic circuits.

EE 202 Circuit Analysis II

Sinusoidal steady-state analysis, phasors. Three-phase circuits. Coupled inductors. Frequency response. Linear time-invariant dynamic circuits: state equations, natural frequencies, complex frequency domain analysis.

EE 362 Feedback Control Systems

Mathematical modeling: Transfer functions, state equations, block diagrams. System response; performance specifications. Stability of feedback systems: Routh-Hurwitz criterion, principle of argument, Nyquist stability criterion, gain margin and phase margin. Design of dynamic compensators. Analysis and design techniques using root-locus. State-space techniques: Controllability, observability, pole placement and estimator design. Discrete-time control systems.