Teaching

I have been involved in the following courses at the University of Liège:

The course alternates between notions related to the C language and to algorithmic patterns. The main themes tackled are the following: basic syntax and semantic of the C language, simple algorithms (linear run of an array, cumulative mathematical operations), dividing a problem into sub-problems, basic data structures (record, array, string, files) and program modularity (procedure/function, global variable). The structure of the course is as follows:

Chapter 1: Block, Variables, Simple Instructions

Chapter 2: Control Statements

Chapter 3: Data Structures

Chapter 4: Code Modularity

Chapter 5: Introduction to Matlab®


Having access to abundant energy is a key component of our societies' lifestyle. The energy transition amounts in abolishing the dependency of our societies to finite and non-renewable energy resources. Is this manageable? Applied mathematics may help us imagine the future...


Maintaining a system in a specific operating condition is a common task, both in technical applications as well as in the life sciences. Examples are of such control applications are autopilots, Electronic Stability Control, homeostasis, temperature control in a room (thermostat) or in the human body (thermoregulation, etc). A brief overview of the content of this course:

Modelling and control of linear feedback control systems

Open-loop and closed-loop concepts

Advantages and drawbacks of feedback control

Analysis and synthesis of state-space models: controllability and observability

Separation principle

Frequency methods for loop analysis (Bode, Nyquist, loop-shaping, sensitivity functions, performance limitations)

PID and lead-lag control

State observer

Static and dynamic state feedback

Robustness and performance

All details can be found here: https://sites.google.com/site/raphaelfonteneau/syst003


Numerical analysis is at the boundary between Mathematics and Computer Science. It consists in studying how to practically obtain in a computer different mathematical concepts studied in other courses.

There are two main types of problems studied by numerical analysis:

- how to actually compute results for which an analytical expression exists but that can be obtained more or less accurately depending on the selected method

- how to compute solutions of real problems for which no analytical solution is known but that can be approximated using a computer.

The course is structured in four main chapters.

Chapter 1: Polynomial interpolation and regression

Chapter 2: Numerical derivation and integration

Chapter 3: Numerical linear algebra and basic linear programming

Chapter 4: Non linear systems and some basics about non linear optimization


Stochastic processes allow to model system which behavior is only partially predictable. Their theory is based on the probability calculus and statistics. They have multitudinous applications: various questions in telecommunications, signal processing and adaptive control, and filtering. The objective of this cours is to introduce the basic concepts used for studying such systems, by calling for examples from engineering.

The course is composed of three main parts.

Part 1. Markov chains and hidden Markov chains.

Part 2. Vectors of Gaussian random variables and estimation theory.

Part 3. The Kalman filter (linear systems, gaussian noise processes)