Master of Mathematics in Applied Mathematics - Control and Dynamical Systems

University of Waterloo

This field is centred on the subject of differential equations, which provide the basis for mathematical models in many fields including the physical sciences, engineering, the life sciences and finance. This subject is broad, ranging from the traditional ordinary and partial differential equations, to the more modern delay and stochastic differential equations. The two aspects of the subject that we emphasize are control theory and dynamical systems.Firstly, control theory refers to the process of influencing the behaviour of a physical or biological system to achieve a desired goal, primarily through the use of feedback. The governing equations of the system in question are differential equations of various types. Secondly, the theory of dynamical systems deals with the qualitative analysis of solutions of differential equations on the one hand and difference equations on the other hand. The latter comprises the subfield of discrete dynamical systems, which has applications in diverse areas, for example biology and signal processing. A recent development is the notion of hybrid dynamical system, which allows the interaction of discrete events and continuous dynamics, thereby providing a natural framework for mathematical modeling of complex reactive systems or intelligent systems, in which physical processes interact with man-made automated environments.