Approved Advanced Engineering Mathematics courses

(Other courses can be added to this list, with prior approval by Graduate Affairs Committee of the Washkewicz College of Engineering. Course instructors please contact Director of the Doctoral programs for procedures.)

The following three courses currently exist, with changes in name only:

ESC 702 Advanced Optimization (4 credit hours). Methods of optimization for engineering systems; classical optimization, Taylor’s theorem, Lagrange Multipliers, and Kuhn-Tucker theorem; direct methods, Newton and quasi-Newton methods, penalty and Barrier methods, linear and nonlinear programming.

ESC 704 Stochastic Systems (4 credit hours). Prerequisite: Engineering Statistics. Optimization in engineering economics; application of renewal theory; inventory and Markov decision models; Bayesian decision analysis.

ESC 706 Advanced Partial Differential Equations (4 credit hours). Engineering applications and solution techniques for partial differential equations; variational derivation of differential equations and boundary conditions; Hamilton’s principle and Lagrange’s equation; numerical methods and computer solutions for differential equations.

Other Approved Alternatives:

BME 570/770 Biomedical Signal Processing (3-0-3). Prerequisite: Graduate standing in Engineering or permission of instructor. Signals and biomedical signal processing; the Fourier transform; image filtering, enhancement, and restoration; edge detection and image segmentation; wavelet transform; clustering and classification; processing of biomedical signals; processing of biomedical images.

CVE 604/704 Elasticity (4-0-4). Prerequisite: CVE 513. Elasticity topics include tensor algebra, fundamentals of stress analysis, fundamentals of deformation theory, thermoelastic constitutive relationships, uniqueness of solution, Airy’s stress function, and various solution techniques for two-dimensional problems.

EEC 643/743 or MCE 693/793 Nonlinear Systems (4-0-4) Prerequisite: EEC 510. State-space and frequency domain analysis and design of nonlinear feedback systems. Methods include Liapunov’s stability analysis, singular perturbations, describing functions, and absolute stability criteria. Feedback linearization and variable structure/sliding mode control.

EEC 645/745 Intelligent Control Systems (4-0-4) Prerequisite: EEC 510. Artificial intelligence techniques applied to control system design. Topics include fuzzy sets, artificial neural networks, methods for designing fuzzy-logic controllers and neural network controllers; application of computer-aided design techniques for designing fuzzy-logic and neural-network controllers.

EEC 644/744 Optimal Control Systems (4-0-4) Prerequisite: EEC 510. Introduction to the principles and methods of the optimal control approach: performance measures; dynamic programming; calculus of variations; Pontryagin’s principle; optimal linear regulators; minimum-time and minimum-fuel problems; steepest descent; and quasi-linearization methods for determining optimal trajectories.

EEC 693/793 Population-Based Optimization (4-0-4) This course discusses the theory, history, mathematics, and applications of population-based optimization algorithms, most of which are based on biological processes. Some of the algorithms that are covered include genetic algorithms, evolutionary computing, ant colony optimization, biogeography-based optimization, differential evolution, and artificial immune systems. Students will write computer-based simulations of optimization algorithms using Matlab. After taking this course the student will be able to apply population-based algorithms using Matlab (or some other high -evel programming language) to realistic engineering problems. This course will make the student aware of the current state-of-the-art in the field, and will prepare the student to conduct independent research in the field.

ESC 794 Selected Topics:  Mathematics of Control and Systems Theory (4-0-4) 

Selected mathematical topics to prepare the student for independent, advanced study in systems and control theory and related fields, fundamental notions, real analysis methods, and geometric methods. Open to doctoral students only unless permission is obtained from the instructor. One course in linear algebra and at least one graduate course in control systems are required.