Web page of Charles Dapogny

This mini-course was given at the occasion of the SIAM International Meshing Roundtable 2023 in Amsterdam. Many thanks to Franck Ledoux for this kind invitation! You may download:

The syllabus of the course.
The slides of the course (heavy .pdf file!).

This refresher course is intended for students entering the M1 MSIAM in Grenoble; it is aimed at recalling fundamental concepts about differential calculus, as well as important applications, notably the fixed point theorem, the implicit function theorem, etc.

The lecture notes containing an extended version of the course can be downloaded here.

This mini-course was given at the occasion of the Master Class: PDE, Optimization and data in Strasbourg. Many thanks to the organizers for their kind invitation! You may download:

The syllabus of the course (in French).
The slides of the lectures (heavy .pdf file!).

This course is part of the M2-MSIAM of the University of Grenoble. It is prepared jointly with Eric Bonnetier.

Click here to visit the dedicated webpage of the course.
An adapted version from this course will be proposed online for students of the University of Tripoli (Lebanon); click here to get the schedule.

This mini-course was given at the occasion of the POEMS Team seminar in Paris. The slides of the course are available here.

This mini-course was given at the occasion of the GDR MOA annual days. You may download:

The syllabus of the course.
The slides of the lectures (heavy .pdf file!).
The classnotes of the hands-on sessions.
The link to the GitHub repository containing all the material from the course, including the source code of all the examples proposed in the hands-on session.

Les slides de la présentation. Un grand merci à Nicolas Nguyen pour son accueil chaleureux et son enthousiasme communicatif !

This course is part of the larger course Level-set, Optimal Transport, application to image analysis, taught by Emmanuel Maitre.
The slides of the course.
Here is a set of notes devoted to the topic of the course.

See the page of the course on the website of Pascal Frey.

Office hours: every Wednesday (15:00 - 16:00), and Thursday (9:00 - 10:00) in my office (344).
Here is a provisional syllabus for the course

Here is the list of homeworks; NO late homework will be considered, whatever the reason !

Homework 1: Revisions around sets, functions, and the induction principle Assigned 09/09/2014, due 09/16/2014.
Homework 2: Countability, and the set of real numbers Assigned 09/18/2014, due 09/25/2014.
Homework 3: Convergence and arithmetic operations between sequences Assigned 09/25/2014, due 10/02/2014.
Homework 4: Cauchy sequences, subsequences and monotone sequences Assigned 10/02/2014, due 10/09/2014.
Homework 5: Limits of functions: definition and operations Assigned 10/09/2014, due 10/16/2014.
Homework 6: Limits of functions (continued) and continuity Assigned 10/16/2014, due 10/23/2014.
Homework 7: Continuous function: definition and operations Assigned 10/23/2014, due 10/30/2014.
Homework 8: Open, closed and compacts sets; uniformly continuous functions Assigned 10/30/2014, due 11/06/2014.
Homework 9: Properties of continuous functions on compact and connected sets Assigned 11/06/2014, due 11/13/2014.
Homework 10: The Intermediate-Value Theorem and differentiable functions Assigned 11/13/2014, due 11/20/2014.
Homework 11: Rolle's theorem and the Mean-Value Theorem Assigned 11/20/2014, due 12/02/2014.

The first midterm will take place on the 10/09/2014; here and here are sheets of additionnal exercises to help you in your preparation.

The second midterm will take place on the 11/25/2014; here is a sheet of additionnal exercises to help you in your preparation. Follow this link for a solution to Exercise 7.

The final exam is scheduled on the 12/16/2014; here is a sheet of additionnal exercises to help you in your preparation.

The workshop sessions are organized by M. Balasubramanian. Here is the list of workshop exercises:

Office hours: every Tuesday and Wednesday 9:00 a.m. - 10:00 a.m, in my office (344).
Here is a provisional syllabus for the course

Here is the list of homeworks; watch out: NO late homework will be considered, whatever the reason !

Homework 1: elementary notions, and the method of characteristics Assigned 01/28/2014, due 02/04/2014.
Here is also a partial correction.
Homework 2: partial differential equations from physics and boundary conditions Assigned 02/04/2014, due 02/11/2014.
Homework 3: partial differential equations from physics (continued), and second-order linear PDE Assigned 02/11/2014, due 02/20/2014.
Homework 4: the wave equation on the real line Assigned 02/20/2014, due 02/27/2014.

Here

The first midterm proposed on 03/04/2014.

Here

Homework 5: the heat equation on the real line and a first glance at the method of separation of variables Assigned 03/11/2014, due 03/25/2014.

Here

Homework 6: The method of separation of variables (continued), and first encounter with Fourier series Assigned 03/25/2014, due 04/01/2014.

Here

Homework 7: More Fourier series Assigned 04/01/2014, due 04/08/2014.

Here

The second midterm proposed on 04/15/2014.

Here

Homework 8: Convergence of Fourier series and the L^2 theory Assigned 04/08/2014, due 04/22/2014.

Important announcement:

Here

Homework 9: The method of separation of variables with inhomogeneous data and the Laplace equation Assigned 04/22/2014, due 04/29/2014.

Here

Here is a list of complementary material, whose study may come in handy in your preparation for the final exam.

Le polycopié de Jean-Yves Chemin

Le mémo de Frédéric le Roux

Les feuilles de td :

Pour vous entraîner, voici les sujets des interrogations des autres groupes de Td : sujet 1 sujet 2, ainsi que leur corrigé respectif : corrigé 1 corrigé 2
Voici également un exercice corrigé proposé par T. Bourgeron pendant l'atelier.

Les sujets de TP

Quelques notes informelles pour vous aider à démarrer les projets

Le canevas de code C dans lequel programmer vos fonctions, ainsi que quelques outils complémentaires

Le morceau de code C pour lire les fichiers de terrains (projet 2)

Les exemples sur lesquels tester vos programmes :

Trois exemples d'images pour le projet 1 : Einstein, J. Von Neumann, et Chaplin
Quatre exemples de terrains pour le projet 2 : le Grand Canyon, crater, ozark, et ntc

2023 - Mini-course: The level set method in connection with meshing

2022 - Refresher: differential calculus and applications

2022 - Mini-course: An introduction to the level set method and its applications

2020 - *: An introduction to shape and topology optimization

2017 - * - Analyse fonctionnelle : du continu au discret

Cours de Sylvain Meignen

2019 - Mini-course: Localized plasmonic resonances and the Neumann-Poincaré operator: homogenization and bowties

2018 - Mini-course: An introduction to shape and topology optimization

2018 (St Brieuc) - Broad audience introduction to shape optimization (in French)

2015 - * : Fall (ENSIMAG) - Mini-course: An introduction to the Level Set method

2012 - 2015 (Medellin, Colombia) - Numerical methods for incompressible fluids

2014 (Fall) - Advanced Calculus I (Math 311)

2014 (Spring) - Elementary partial differential equations (Math 423)

2012 - Topologie et Calcul Différentiel (LM360)

Cours de Jean-Yves Chemin et Frédéric le Roux

2011 - Méthodes d'adaptation pour la simulation numérique (NM491)

Cours de Pascal Frey