Numerical analysis

Summary

This course presents numerical methods for the solution of mathematical problems such as systems of linear and non-linear equations, functions approximation, integration and differentiation, and differential equations.

Content

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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

Learning Outcomes

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

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

Transversal skills

• Use both general and domain specific IT resources and tools
• Access and evaluate appropriate sources of information.

Teaching methods

Ex cathedra lectures, exercices in class and with computers

Expected student activities

• Attendance to lectures
• Exercises resolution
• Resolution of elementary problem with computers

Assessment methods

Written exam. The exam may require the resolution of problems in a computer using Python.

Supervision

Office hours	Yes
Assistants	Yes
Forum	Yes

Resources

Virtual desktop infrastructure (VDI)

Yes

Bibliography

• Course's notes (English and French versions available).
• 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 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.
• J. Rappaz et M. Picasso: "Introduction à l'analyse numérique", PPUR - Collection: Enseignement des mathématiques - 2017

 

Ressources en bibliothèque

• Calcul scientifique / Quarteroni
• Scientific computing with MATLAB and OCTAVE / Quarteroni
• Numerical Mathematics / Quarteroni
• Introduction à l'analyse numérique / Rappaz & Picasso

Notes/Handbook

Available on the Moodle (English and French versions).

Moodle Link

• https://go.epfl.ch/MATH-251_a