# Teaching

​Taous-Meriem Laleg teaches three courses:

• AMCS 370 - Advanced inverse problems (Fall 2012)
This course introduces the mathematical theory of inverse problems. It  gives the basis notions and the difficulties encountered with ill-posed inverse problems. It presents methods for analyzing these problems and gives some tools to solve such problems. This course shows what is a regularization method and introduces different regularization techniques and the basic properties of these methods. Examples of  inverse problems are also provided.
• AMCS 202 - Applied mathematics II (Spring 2011 and summer 2011)
This course gives an overview on im​portant topics in applied mathematics. It starts with a review on linear algebra introducing some basic concepts. Then, it focuses on numerical methods for solving systems of linear equations. These methods are designed to give the expertise necessary to understand and use computational methods for solving scientific problems. We are especially interested in methods for solving systems of linear equations and eigenvalues problems. The second part is dedicated to complex analysis which has many applications to engineering, physics and applied mathematics. We are interested mainly in the properties of complex numbers analytic functions, contour integrals, Cauchy residue theorem and conformal mapping. We introduce also the Fourier and Laplace transforms and/or Ordinary Differential Equations which are important tools in many fields.​
• ME 221B - Control Theory B (Fall 2011)

This course gives basic knowledge for more advanced courses. Students will gain experience in designing feedback control systems by some state variable methods and by using observers. The course begins with a brief review of some basic concepts in control theory such as the state representation, stability, controllability, observability and associated properties. Then, some control techniques for linear systems are presented starting  by the feedback control and pole placement and then the optimal control with a focus on linear quadratic regulator. The concepts of observer and Kalman filter are also introduced with some observers based control techniques. An important property in a control system is also considered, which  is the robustness. This course finishes by an introduction to  control of nonlinear systems. It is embedded of examples issued from physical systems with illustrations in Matlab.