Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 14, 2005.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, November 14, 2005

3:00 pm in 2005 MEL,Monday, November 14, 2005

#### Dynamical Perspectives on Control of Non-Equilibrium Behavior

###### Prashant Mehta (Dept. of Mechanical and Industrial Engineering, UIUC)

Abstract: Complex and chaotic non-equilibrium dynamic behavior occurs in diverse applications. Some common examples are: instabilities in aerospace applications, air-flow dynamics in buildings, non-stationary behavior in networks such as traffic networks or communication networks, dynamic biological phenomena such as replication and folding of DNA. While the field of Dynamical Systems has seen important advances in classification and analysis of such behavior, its impact on applications - particularly in nonlinear control theory - remains an open and exciting area of investigation. In this talk, I will highlight the striking interplay between Dynamics and Control. I will do so with the aid of Lyapunov functions, which are widely used for nonlinear control. I will introduce these functions, review their construction, and highlight some of their inadequacies. By combining ideas from the field of stochastic dynamics with control, I will then propose a generalization for overcoming some of these inadequacies. I will show its applicability to both stability analysis and control of non-equilibrium behavior. Results on computations and future directions for applications will also be provided.

4:00 pm in 245 Altgeld Hall,Monday, November 14, 2005

#### Teaching Mathematics using Mathematica: A Visual Approach

###### Bruce Carpenter (UIUC Department of Mathematics)

Abstract: The Calculus & Mathematica program attempts to actively involve students in their own learning by putting them in a position to acquire mathematical ideas visually. This means using technology to initiate the learning process instead of hanging it on the end of the learning process. This can free students to achieve a better conceptual understanding of the material while still gaining a good knowledge of the methods of problem-solving. Come for a discussion on the benefits of teaching mathematics in the Calculus & Mathematica program and the pedagogical issues involved.