Due to the COVID-19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 45.0 h
Q1
Teacher(s)
Van Schaftingen Jean;
Language
French
Main themes
Sources of numerical errors, direct and iterative methods to solve linear systems of equations, iterative methods to solve non-linear equations, least square approximation, numerical integration.
Aims
At the end of this learning unit, the student is able to : | |
| 1 |
Contribution of the course to learning outcomes in the Bachelor in Mathematics programme. By the end of this activity, students will have made progress in: - Recognise and understand a basic foundation of mathematics. -- Choose and use the basic tools of calculation to solve mathematical problems. -- Recognise the fundamental concepts of important current mathematical theories. -- Establish the main connections between these theories, analyse them and explain them through the use of examples. - Identify, by use of the abstract and experimental approach specific to the exact sciences, the unifying features of different situations and experiments in mathematics or in closely related fields (probability and statistics, physics, computing). - Show evidence of abstract thinking and of a critical spirit. -- Argue within the context of the axiomatic method Recognise the key arguments and the structure of a proof. -- Construct and draw up a proof independently. -- Evaluate the rigour of a mathematical or logical argument and identify any possible flaws in it. -- Distinguish between the intuition and the validity of a result and the different levels of rigorous understanding of this same result. Learning outcomes specific to the course. By the end of this activity, students will be able to: - Understand which are the possible sources of errors in a numerical method. - Solve numerical problems using Matlab. - Apply direct and iterative methods to solve linear systems. - Solve a linear system in the least square sense. - Understand the main idea of some methods of numerical integration. |
Content
- complexity of numerical algorithms,
- floating-point representation, arithmetic and error,
- numerical differentiation and integration,
- solution nonlinear equations,
- solutions of linear systems,
- introduction to numerical integration of ordinary differential equations.
Teaching methods
Due to the COVID-19 crisis, the information in this section is particularly likely to change.
- Theoretical sessions aimed at introducing the fundamental methods and concepts of numerical analysis and motivating them by showing examples and applications, through group discussions and presentation by the professor,
-
Computer lab sessions work to implement and use numerical methods on Python in the SciPy ecosystem, with code and graphics being submitted for evaluation,
-
Online discussion forum.
Evaluation methods
Due to the COVID-19 crisis, the information in this section is particularly likely to change.
- 15% for participation in theory sessions and online discussions,
- 35% for practical assignments submitted,
- 50% for the open book oral exam.
Participation and assignment marks can only be obtained during the course quadrimester and will therefore have their mark attached to all the sessions of the entire academic year.
Online resources
Course materials (syllabus, exercises and practice) will be published on Moodle (https://moodleucl.uclouvain.be/course/view.php?id=10936).
Teaching materials
- Syllabus 2017-2018 et compléments
Faculty or entity
MATH
