Mathématiques

Mathématiques
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

Plan :
1 Préambule sur le calcul tensoriel
2 Espace vectoriel, espace Euclidien
3 Tenseurs —>lien avec la Mécanique des Milieux Continus
4 Espace ponctuel, coordonnées curvilignes, symboles de Christoffel
5 Dérivée covariante, accélération d’une particule, opérateurs différentiels
6 Transport parallèle
7 Géodésiques —>lien avec la tomographie sismique (trajets des ondes de surface) et liens avec la relativité générale (géométrie de l’espace-temps)
8 Polynômes de Legendre (associés)
9 Harmoniques Sphériques —>lien avec la tomographie globale (paramétrisation des modèles) et le géomagnétisme

Table of contents :
1 Preamble on tensor calculus
2 Vectorial spaces, Euclidean space
3 Tensors —>link with Continuum Mechanics
4 Point space, curvilinear coordinates, Christoffel symbols
5 Covariant derivative, acceleration of a particle, differential operators
6 Parallel transport
7 Geodesics —>link with seismic tomography (surface-wave ray paths) and links with general relativity (space-time geometry)
8 Legendre polynomials (associate)
9 Spherical harmonics —>link with global tomography (model parameterization) and geomagnetism

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

  • Comprendre des concepts mathématiques clés qui sont utiles, par exemple, en mécanique des milieux continus, en tomographie sismique à l’échelle globale, en géomagnétisme, etc.
  • Raisonner : démonstration, raisonnement logique, etc.
  • Understanding key mathematical concepts which are useful, for example, in continuum mechanics, global seismic tomography, geomagnetism, etc.
  • Arguing : proofs, logical reasoning, etc.

Compétences visées

L'objectif est d'apprendre, au niveau "ingénieur-géophysicien", certains concepts mathématiques tels que : le lanage des tenseurs, la géométrie différentielle (géodésiques sur la sphère, etc), certaines fonctions spéciales (polynômes de Legendre associés, harmoniques sphériques, etc).

The main objective of this module is to learn, at the "geophysicist-engineer" level, some mathematical concepts such that : tensors, differential geometry (geodesics on the sphere, etc), some special fonctions (associate Legendre polynomials, spherical harmonics, etc).

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.