Elements of this framework include real and complex function theory, ordinary and partial differential equations, integral equations, differential geometry, tensor analysis, special functions, variational methods, and probability theory. Department members continually use, and sometimes further develop, all of these tools in their research. Almost every engineering or physical system needs control in some form or another to improve performance as well as robustness with respect to disturbances and model uncertainties. Our research interests include the fundamental techniques for design and analysis of control systems for such diverse applications. In recent years, interest has developed in exploring the application of techniques developed in the Artificial Intelligence field to the control systems design problem.
Examples involve application of artificial neural networks and genetic programming.
In addition, we continue to explore more conventional optimization-based methods. The Department of Applied Mathematics, in cooperation with departments in the College of Engineering, offers a wide spectrum of courses that can be tailored to the specific research goals of the student in support of a control sciences program. Modern control sciences research is strongly mathematical and rests on numerous applied mathematics topics, thus integrating classical analysis techniques with computer modelling, simulation, and numerical analysis techniques. Geophysical Fluid Dynamics C. S. Bretherton , W. O. Criminale , P. J. Schmid , K. K. Tung Mathematical models play a crucial role in our understanding of the fluid dynamics of the atmosphere and oceans. Our interests include mathematical methods for studying the hydrodynamical instability of shear flows, transition from laminar flow to turbulence, applications of fractals to turbulence, and large-scale nonlinear wave mechanics.