Professor in Applied Mathematics - Computational Sciences at INSA Toulouse
Member of Institut de Mathematiques de Toulouse.
Open Online Courses
A few platforms
L'universite numerique: Open Moodle offering numerous courses in French.Open INSA: online self-sufficient courses offered by INSA group.
OpenINSA, in partnership with Open Classrooms.
Unisciel: a French OOC platform.
FUN : a French MOOC platform.
Canal-U: an academic french webTV.
De nombreuses leçons sont produites par les collègues de l'INSA sur notre plateforme Moodle de l'INSA Toulouse, y compris sous forme de vidéos.
A few Open Online Courses personaly produced
These courses are those I have created the last decade from more or less advanced existing pre-material (books, chapters, former local manuscripts etc). Today I teach a few of tehses courses only. However, all of them have been ransfered to with all self-suffient material (Self-Regulated Learning). For each course, manuscripts, exercises with corrections, programming practicals (with solution codes) for scientific computing courses , and self-training quizzes are available on a Moodle page.Master's level courses are in English; Bachelor's level (Licence en français) are in French.
Master's level
- Inverse Problems, Control, Data Assimilation & Model learning (Master Sc., PhD, research scientists).
VDA: coupling physically-informed models and data sets. (click to go to the dedicated course webpage).
The complete textbook whcih should converge to a final version...
Contents: Basics of inverse problems, regression problems, regularization,data assimilation methods (sequential, variational, Bayesian inferences and their connections), variational approaches (optimal control, Variational DA), and model learning.
External ressources - courses are proposed too, in particular one presenting a few links between machine learning - neural networks and data assimilation.
- Finite Element Modeling & Models reductions (Master Sc.).
The course manuscript.
Content FEM: math. analysis (Lax-Milgram's theory); classical FE schemes - coding; error estimations; constraints & Lagrangian multipliers and reduced models (POD).
Content Model reductions: POD, hybrid POD-Neural Networks methods.
The complete course page on INSA Moodle platform. login : anonymous; pass: insa-fem.
Cycle Préparatoire / Licence (BSc.)
- Outils mathématiques: séries de Fourier, Dirac, convolution, transformées de Fourier, transformée de Laplace (cours destinés à un large public plutôt hors filière maths, niveau L2).
Manuscripts: séries de Fourier, le Dirac, transformees de Fourier, transformée de laplace.
Contenu : Séries de Fourier; Transformée de Fourier, Dirac, convolution; Transformée de Laplace.
Le cours complet est disponible sur le Moodle du Groupe INSA (login: anonymous, mdp: insa-fourier) ou encore sur l'universite numerique.
- Méthodes numériques pour l'ingénieur (niveau L2-L3) -vidéos-:
The complete course on INSA group Moodle platform (4 authors). login: anonymous; mdp: insa-an.
A few videos: Equations non linéaires; Méthodes itératives de résolution de systèmes linéaires; Méthodes de descente; Moindres carrés.
- Analyse 1 (niveau L2). Equivalences de fonctions, développements limités, développements asymptotiques, intégration.
The course manuscript.
The complete course on INSA group Moodle platform. login: anonymous; mdp: insa-analyse1.
- Analyse 2 (niveau L2). Fonctions à plusieurs variables: dérivation, intégration, premiers pas en optimisation, changements de variables.
The course manuscript.
The complete course on INSA Moodle platform. login: anonymous; mdp: insa-analyse2.
- Introduction aux modèles d'EDP et leur résolution numérique par Différences Finies (niveau L3) -vidéos-:
The course page on INSA group Moodle platform. login: anonymous; ; mdp: insa-introedpdf.
A few videos: Formules aux Différences Finies (DF) et premier schéma numérique; EDP classiques, équation de Poisson-Laplace; Schémas aux Différences Finies pour l'équation de Poisson.