Mathématiques pour la physique

The course is divided into three parts : numerical methods (48h), group theory (42h) and partial differential equations (30h).

Numerical methods :
Introduction to numerical methods for the resolution of partial differential equations
1. Integration of ordinary differential equations
2. Differentiation by the method of finite difference
3. Resolution of partial differential equations
4. Iterative methods for the inversion of linear equations
5. Spectral methods: Fourier series and Chebyshev polynomials

Group theory :
1. Introduction and motivation
2. Group theory, representations and algebras
3. Rotations: SO(3) and SU(2) groups and algebras
4. Space-time transformations: Lorentz and Poincaré groups

Partial differential equations :
1. Classification of linear partial differential equations of order 2
2. Introduction to hyperbolic, elliptic, parabolic equations
3. Partial differential equations of order 1
4. Introduction to the theory of distributions

Numerical methods :
- Formulate a numerical method for the resolution of partial differential equations
- Write a program in the Python language to solve a large range of problems described by partial differential equations
- Usage of programming tools including: jupyter notebook, numpy / scipy / matplotlib packages, git / github.

Group theory :
- Master the notions of group and algebra
- Become familiar with the representations of the group of rotations and of space-time transformations, in view of their many uses in physics

Partial differential equations :
- Recognize the different types of partial differential equations of order 2
- Solving some specific equations (separation of variables, Green functions, equations of order 1)

Required and corequired courses

Numerical methods :
Classes with integrated practical exercises (the exercice session may be taught in English but additional explanations may always be sought in French is needed)

Group theory :
classes and exercises

Partial differential equations :
classes and exercises, personal work

References, bibliography, and recommended reading

- Syllabus
- Université virtuelle

Contacts

Analyse numérique : Prof. B. Knaepen, bernard.knaepen@ulb.be
Théorie des groupes : rargurio@ulb.ac.be
Équations aux dérivées partielles : clement.cerovecki@ulb.be
https://uv.ulb.ac.be/course/view.php?id=92718

Campus

Plaine

Method(s) of evaluation

• written examination
• Oral examination
• Other

written examination

Oral examination

Other

Numerical methods :
- Written exam on the course material and exercise sessions

Group theory :
- Oral exam on the course material and the exercises

Partial differential equations :
- Written closed book exam on the course material and the exercises

Mark calculation method (including weighting of intermediary marks)

Numerical methods :
Written exam: 100%

Group theory :
Oral exam : 100%

Partial differential equations :
- Written exam : 100%

If the marks obtained for all the parts of the course are >= 10, the final mark will be the weighted average of the marks obtained in each of the three parts. Otherwise, the final mark will be the lowest mark among the three marks obtained.

Language(s) of evaluation

• french
• (if applicable english )