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Mathématiques pour la physique
Course teacher(s)
Riccardo ARGURIO (Coordinator), Denis BONHEURE, Clément Cerovecki and Bernard KNAEPENECTS credits
10
Language(s) of instruction
french
Course content
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
Objectives (and/or specific learning outcomes)
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 py 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)
Prerequisites and Corequisites
Required and corequired courses
Teaching methods and learning activities
Numerical methods :
Classes with integrated practical exercises / flipped classes / personal work.
Group theory :
classes and exercises, personal work
Partial differential equations :
classes and exercises, personal work
References, bibliography, and recommended reading
- Syllabus
- Université virtuelle
Other information
Contacts
Analyse numérique : Prof. B. Knaepen, bernard.knaepen@ulb.be
Théorie des groupes : rargurio@ulb.ac.be
Équations aux dérivées partielles : julie.distexhe@ulb.be
https://uv.ulb.ac.be/course/view.php?id=92718
Campus
Plaine
Evaluation
Method(s) of evaluation
- Other
Other
Numerical methods :
- Written exam on the course material
- One homework to be handed in before the winter holidays. This homework cannot be presented again in second session. The mark obtained in first session is automatically transferred to the second session.
Group theory :
- Written exam on the course material and the exercises
- Oral exam on the course material
Partial differential equations :
- Personal works during the period of teaching
- Oral exam on the course material and the exercises
Mark calculation method (including weighting of intermediary marks)
Numerical methods :
Written exam: 75%
Homework (project): 25%
Group theory :
Written exam: 50%
- Oral exam : 50%
Partial differential equations :
- Oral exam : 50%
- Personal works : 50%
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 )