# 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 software.

#### Learning Prerequisites

##### Required courses

Analysis, Linear Algebra

#### Learning Outcomes

• 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 with computer using MATLAB sofware. For both, the theory and exercises lectures a videoconference system will be used.

#### Expected student activities

• Class attendance.
• Solution of proposed exercises.
• Solution of problems using MATLAB.

#### Assessment methods

Written exam at the end of the semester.

#### Supervision

 Office hours Yes Assistants Yes Forum Yes

#### 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 as well as the handwritten notes used during the theory lectures. The recorded videos of the theory lectures will also be available to the sudents.

### In the programs

• Semester
Spring
• Exam form
Written
• Credits
4
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
4
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
4
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Passerelle HES - EL, 2020-2021, Spring semester
• Semester
Spring
• Exam form
Written
• Credits
4
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Passerelle HES - GM, 2020-2021, Spring semester
• Semester
Spring
• Exam form
Written
• Credits
4
• Subject examined
Numerical analysis
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 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