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.

## Keywords

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

## Required courses

Analyse, Algèbre linéaire

## 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

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

## Notes/Handbook

Lecture notes will be provided.

## 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

 Lu Ma Me Je Ve 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