MATH-251(a) / 3 crédits

Enseignant: Antolin Sanchez Pablo

Langue: Anglais


Summary

This course offers an introduction to numerical methods for the solution of mathematical problems as: solution of systems of linear and non-linear equations, functions approximation, integration and differentiation and solution of differential equations.

Content

Keywords

Numerical algorithms; polynomial interpolation; numerical integration; numerical linear algebra; numerical solution of ODEs; iterative methods.

Learning Prerequisites

Required courses

Analyse, Algèbre linéaire

Recommended courses

Programmation Matlab (GC)Informatique pour l'ingénieur (SIE).

Important concepts to start the course

Analysis, linear algebra and programming.

 

 

Learning Outcomes

By the end of the course, the student must be able to:

  • Choose a numerical method for solving a specific problem.
  • Interpret obtained numerical results from a theoretical perspective.
  • Estimate numerical errors.
  • Prove theoretical properties of numerical methods.
  • Implement numerical algorithms.
  • Apply numerical algorithms to specific problems.
  • Describe numerical methods.
  • State theoretical properties of mathematical problems and numerical methods.

Transversal skills

  • Use a work methodology appropriate to the task.
  • Use both general and domain specific IT resources and tools
  • Access and evaluate appropriate sources of information.

Teaching methods

Ex cathedra lectures; exercises in class and with computer using MATLAB/OCTAVE sofware.

 

 

 

Expected student activities

  • Class attendance.
  • Solution of exercises.
  • Solution of problems using MATLAB/OCTAVE sofware.

Assessment methods

The exam may require to use a computer and MATLAB/OCTAVE software.

 

Supervision

Office hours Yes
Assistants Yes
Forum No

Resources

Virtual desktop infrastructure (VDI)

Yes

Bibliography

In English:

  • Lecturer notes.
  • A. Quarteroni et F. Saleri et P. Gervasio: « Scientific Computing with MATLAB and OCTAVE », Springer, 2014, ISBN 978-3-642-45367-0.
  • A. Quarteroni, R. Sacco et F. Saleri : « Numerical Mathematics », Springer, 2007, ISBN 978-3-540-49809-4.

In French:

  • Lecture notes.
  • A. Quarteroni, P. Gervasio et F. Saleri : « Calcul Scientifique : Cours, exercices corrigés et illustrations en MATLAB et OCTAVE », Springer, 2010, ISBN 978-88-470-1676-7.
  • A. Quarteroni, R. Sacco et F. Saleri : « Méthodes Numériques - Algorithmes, analyse et applications », Springer, 2007, ISBN 978-88-470-0495-5.
  • J. Rappaz et M. Picasso: "Introduction à l'analyse numérique", PPUR - Collection: Enseignement des mathématiques - 2em édition - 2011

Ressources en bibliothèque

Notes/Handbook

Lecture notes will be provided.

Videos

Dans les plans d'études

  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Numerical analysis
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Numerical analysis
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Numerical analysis
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22