Analyse numérique

Analyse numérique
Diplôme d'ingénieur de l'École et observatoire des sciences de la Terre (EOST)Parcours Diplôme d'ingénieur de l'EOST

ComposanteÉcole et observatoire des sciences de la Terre (EOST)

Description

Représentation des nombres en machine -- Le standard IEEE-754

Erreurs d'arrondi -- Stabilité des algorithmes

Algèbre linéaire

Équations non linéaires à une et plusieurs variables

Intégration

Transformée de Fourrier rapide (FFT)

Équations différentielles ordinaires (ODE)

Équations aux dérivées partielles (PDE): introduction aux différences finies



Representation of machine numbers -- The IEEE-754 standard

Roundoff errors -- Stability of algorithms

Linear algebra

Nonlinear equations in one or several variables

Integration

Fast Fourier transform (FFT)

Ordinary differential equations (ODE)

Partial differential equations: introduction to finite differences



A la fin de ce cours, vous serez capable de :

- comprendre les modes d'emploi des logiciels généraux afin de pouvoir les utiliser de façon appropriée;

- aborder plus facilement les livres d'analyse numérique afin d'approfondir le cours;

- eventuellement développer des méthodes spécifiques si aucune n'existe pour un problème particulier;

- analyser les raisons qui font qu'une méthode ou un logiciel produit des résultats aberrants et avoir des pistes pour y remédier.



- understand the documentation of general softwares so as to be able to use them appropriately;

- be able to read numerical analysis books when going beyond the lecture is needed;

- possibly develop specific methods if none exist for some problem;

- analyze why a method leads to aberrant results and have ideas about possible ways around.

 

Compétences visées

L'analyse numérique est la discipline qui s'intéresse à la résolution de problèmes par des méthodes numériques. L’objectif de cette UE est d’en acquérir les notions et le vocabulaire de base, qui permettront l'utilisation des logiciels généraux, voire le développement de méthodes spécifiques.


Numerical analysis studies the numerical methods used for solving various problems. The goal is to grasp the basic concepts and vocabulary at play in order to use general softwares, and potentially develop specific methods.

 

School regulations

The curriculum includes three years of study: admissions, the organisation of studies, assessments, placements and vivas, graduation and international exchanges are all explained in the current school rules (pdf).

First and second year courses

First and second year courses

  • General modules: mechanics, geology, mathematics, IT, digital analysis, signal processing, inverse methods.
  • Geophysical methods: physics of the Earth, seismology, seismic modelling and imaging, geodesy, gravimetry, potential methods, geomagnetism, electromagnetism, rock physics and fracture, hydrology.
  • Practical work: geophysical measurements in the field (photo) and in the laboratory, geology field placements in the Alps.
  • Languages and economic and social sciences: English, modern language 2, economics, industrial property, management, sustainable development, ethics, quality, company health and safety
  • IT and research projects, shared with the first year of the master’s degree
  • Summer placements at a laboratory or company, with numerous opportunities abroad (international placement contact: Mike Heap)

Third year course

Students have a choice of 3 specialisations in the third year:

  • Geophysics applied to the exploration and production of raw materials: seismic and hydrodynamic characterisation of reservoirs, seismic processing and interpretation, potential methods.
  • Geophysics applied to geotechnics: geotechnics and the resistance of materials applied in civil engineering, geomechanics, hydrogeophysics, electromagnetic methods, earthquake.
  • Hydrogeology, hydrogeochemistry, hydrogeophysics (HydroG3).

Additional teaching:

  • Languages and economic and social sciences: English, energy economy, company strategy and structure.
  • Geophysics field camp in Alsace (photo).  Here are images of a normal fault in the Rhine Graben taken by students.
  • 6-month industry placement culminating in the writing of a dissertation and a viva before a jury in order to obtain the engineering degree. The placements are carried out all over the world.