# Coursebooks

## Numerical analysis

Kressner Daniel

English

#### Summary

Construction and analysis of numerical methods for the solution of problems from linear algebra, integration, approximation, and differentiation.

#### Content

- Representation of numbers on computers

- Interpolation, numerical integration and differentiation

- Direct and iterative methods for the solution of large systems of equations

- Fourier transform and data compression

#### Keywords

numerical algorithms

numerical linear algebra

#### Learning Prerequisites

##### Required courses

Analysis I and II

Linear Algebra

##### Recommended courses

Elements of scientific programming

#### Learning Outcomes

By the end of the course, the student must be able to:
• Choose a convenient method to solve a specific problem
• Interpret the computational results in view of the existing theory
• Estimate numerical errors
• Apply numerical algorithms to solve specific problems

#### Transversal skills

• Use a work methodology appropriate to the task.
• Give feedback (critique) in an appropriate fashion.
• Use both general and domain specific IT resources and tools
• Access and evaluate appropriate sources of information.

#### Teaching methods

Ex cathedra lectures and exercises in the classroom and on the computer

#### Expected student activities

Attendance of lectures

Doing exercises

Implementing simple programming tools

Solving basic applied mathematics problems

#### Assessment methods

'Form of examination

17% project or homework. 83% exam.

#### Resources

##### Bibliography

Lecture notes accompaying the course will be provided.

• A. Quarteroni, R. Sacco et F. Saleri : « Méthodes Numériques Algorithmes, analyse et applications » Springer, 2007, ISBN 978-88-470-0495-5.A.
• Quarteroni, R. Sacco et F. Saleri : « Numerical Mathematics » Springer, 2007, ISBN 978-3-540-34658-6.A.
• Quarteroni et F. Saleri : « Calcul Scientifique : Cours, exercices corrigés et illustrations en MATLAB et OCTAVE », Springer, 2006, ISBN 978-88-470-0487-0. Edition Française

#### Prerequisite for

Computational linear algebra

Numerical integration of dynamical systems

Other Master courses in numerical analysis and applied mathematics

### 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

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