Teaching

I teach mainly in the Department of Mathematical engineering and have given classes in the Departments of

Mechanics, Thermodynamics and Chemistry. I also teach calculus and mathematics projects for second year undergraduates.

Finally I also supervise about three or four projects per year and have mentored students in industrial modeling weeks.

Perturbations (5th year Engineering mathematics)

Many systems of algebraic equations or evolution problems arising in physics, mechanics or biology have parameters with very different orders of magnitude. The simplest case is when there is a small parameter, the others being of order one. It is then reasonable to approach a solution of the initial problem starting from a solution of the problem where the small parameter is set to zero. The course illustrates this idea for differential equations and partial differential equations. We study the local analysis of fixed points for differential equations and maps ,

the local analysis of fixed points for partial differential equations, inhomogeneous linear partial differential equations and the Fredholm alternative.

We consider the perturbation of symetric matrices and self-adjoint operators and introduce the notions of regular and singular perturbations. We conclude with the method of multiple scales and show how it leads to the Korteweg de Vries equation and nonlinear Schrodinger equation for nonlinear dispersive partial differential equations.

Nonlinear analysis and Inverse Problems (5th year Engineering mathematics)

The field of inverse problems has developed rapidly over the past twenty years, driven mainly by applications. Partly because of this there is no unified theory of these problems, there are rather methods that are adapted to the different situations. We present a panorama of the field discussing first the direct and inverse scattering theory in one dimension where the formalism is well developed. After that we consider linear inverse problems and introduce the notion of regularization to treat ill-posed problems.

Introduction to scientific computing with Fortran and UNIX (3rd year Engineering mathematics).

We present a methodology to solve simple scalar problems in scientific computing using the Fortran language in the UNIX environment. The goal is to develop simple and portable programs. These two qualities are essential to guarantee the life of a program that must be used by several people on different machines. An efficient programmer must know how to use the possibilities of the operating system and not only one or a few programing languages. The UNIX operating system has been generalized to all computer architectures. This is why we describe it in detail taking the user point of view. We also show how to use it at the different stages of program development.

Mathematics projects (2nd year engineering students)

The students work in groups of three or four on problems of dynamics. They adapt numerical codes and analyze the solutions of maps and simple ordinary differential equations in the plane.

Introduction to Numerical analysis (3rd year Engineering)

This is a basic numerical analysis course with practical examples in Fortran and Matlab. The topics covered are interpolation, approximation, the solution of linear systems ( Gauss, LU, iterative methods), the stability of a fixed point iteration, calculations of extremal eigenvalues, Newton's method and bisection, integration methods, the intégration of differential equations by Runge-Kutta and predictor-correctors correctors.

Numerical analysis of partial differential equations (3rd year Engineering)

Classification of second order partial differential equations, methods of characteristics, Burger's equation (notion of shocks). Finite differences and finite volume methods, stability and consistency.

Mechanics of vibrations (4th year Mechanical Engineering)

This course introduces vibrations in mechanical systems, standard and parametric resonances and

models of cristals.

Modeling of physical systems (4th year engineering Mathematics)

We present different evolution models in their physical context and analyze them. I also present Lagrangian mechanics. The emphasis is on qualitative arguments, methods of solution and symmetries.

Mathematical methods for physics (3rd year Mechanical Engineering)

Elements of analysis (sequences, series), complex analysis, Taylor and Laurent series, residues and

applications, principal part of an integral. Fourier transform

International classes:

Time-series analysis for dynamical systems University of Crete, Heraklion, Mars 1992.

Perturbation methods for integrable equations, ``Institute of Mathematical Modelling'', Technical University of Danemark, Novembre 1995 et 1997.