# Coursebooks

## Numerical analysis

#### Lecturer(s) :

Antolin Sanchez Pablo

English

#### 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

• Iterative methods for solving non-linear equations.
• Polynomial approximation: interpolation and least square methods.
• Numerical integration and differentiation.
• Solution of systems of linear equations: direct and iterative methods.
• Numerical approximation of differential equations.
• Introduction to MATLAB/OCTAVE software.

#### Keywords

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

#### Learning Prerequisites

##### 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

#### Resources

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.

### In the programs

• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Passerelle HES - SIE, 2018-2019, Autumn semester
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
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
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German