Analysis

Analysis courses in SMA

(last modified 14.04.2016)

Contact person: Professor Joachim Krieger

Bachelor (1st and 2nd years):

• Analyse I, II, III, IV
• Espaces métriques et topologiques

Bachelor (5th and 6th semesters):

• Espaces de Sobolev et équations aux dérivées partielles elliptiques (BA5, from 2017-2018 on)
• Analyse fonctionnelle I (BA6)
• Equations différentielles ordinaires (BA5)
• Mesure et intégration (BA5)
• Introduction aux équations aux dérivées partielles (BA5)

Master:

• Analyse fonctionnelle II (Spring)
• Harmonic analysis (Spring)
• Linear PDEs I and II (Automn and Spring 2016-2017), replaced by Linear PDEs (in Spring, from 2017-2018 on)
• Calcul des variations (Spring)
• Optimal transport

Description :

During the first and second bachelor years, the students are requested to follow the core courses "Analyse I - IV" as well as the course "Espaces métriques et topologiques" (BA5).
Their contents will be at the basis of all subsequent courses on analysis.

In the third bachelor year, the students are strongly advised to follow the course "Espaces de Sobolev et équations aux dérivées partielles elliptiques" (BA5, from 2017-2018 on).
Indeed, Sobolev spaces are used in many courses taught at the master level, and elliptic problems are the prototypical examples of partial differential equations.
Another course that is strongly recommended is "Analyse fonctionnelle I" (BA6) that presents fundamental concepts about normed linear spaces and linear operators. It is also advised to take the bachelor courses "Equations différentielles ordinaires" (BA5) and "Mesure et intégration" (BA5).
Students wishing to specialize on partial differential equations could also follow "Introduction aux équations aux dérivées partielles" (BA5), and those wishing to develop their knowledge in geometry should take the course on differentiable manifolds "Introduction aux variétés différentiables" (BA5).

At the master levels, there are courses on partial differential equations ("Linear PDEs", "Calcul des variations"), harmonic analysis and functional analysis.
There are also many master courses on related topics, for example a course on Riemannian geometry.

Some other Math courses related to analysis:

• Geometry:
  • Introduction aux variétés différentiables (BA5)
  • Introduction à la géométrie riemannienne (Master)
  • Differential geometry of framed curves (Master)
• Numerical analysis (master):
  • Numerical integration of dynamical systems
  • Numerical approximations of PDEs I and II
  • Numerical methods for conservation laws
• Analysis on groups

Related Minors :

• Computational Science and Engineering