2014 (Fall) - Advanced Calculus I (Math 311)
- 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:
2014 (Spring) - Elementary partial differential equations (Math 423)
- 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 is also a partial correction.
- The first midterm proposed on 03/04/2014.
Here is a correction.
- 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 is a handwritten correction.
- Homework 6: The method of separation of variables (continued), and first encounter with Fourier series Assigned 03/25/2014, due 04/01/2014.
Here is a handwritten correction.
- Homework 7: More Fourier series Assigned 04/01/2014, due 04/08/2014.
Here is a handwritten correction.
- The second midterm proposed on 04/15/2014.
Here is a correction.
- Homework 8: Convergence of Fourier series and the L^2 theory Assigned 04/08/2014, due 04/22/2014.
Important announcement: due to the poor results of Midterm 2, you have a chance to (partially) make up for a possibly bad grade
by achieving a very good grade on Homework 8: obtained points over 8 (out of a total of 10) will be transferred to the grade of Midterm 2 (for a maximum make up of 25 points over 100).
Work hard, using the typed correction of the midterm!
Here is a handwritten correction.
- Homework 9: The method of separation of variables with inhomogeneous data and the Laplace equation Assigned 04/22/2014, due 04/29/2014.
Watch out: the previous version contained a typo in the statement of question 4 of exercise 2 and in that of question 2 of exercise 5, which are corrected in the present one.
Here is a handwritten correction.
- Here is a list of complementary material, whose study may come in handy in your preparation for the final exam.
2012 - Topologie et Calcul Différentiel (LM360)
- 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.
2011 - Méthodes d'adaptation pour la simulation numérique (NM491)
- 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 :