Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 45.0 h
Q1
Teacher(s)
Van Schaftingen Jean;
Language
French
Prerequisites
Prerequirements to follow the course LMAT1151 are the courses LMAT1131 and LMAT1121. In particular: knowledge of basic notions of linear algebra (vector spaces, matrices, eigenvalues and eigenvectors, determinant, rank) and analysis (convergence, continuity and differentiability, integrals).
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. |
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
- error propagation and stability,
- floating-point representation, arithmetic and error
- complexity of numerical
- solutions of linear
- solution nonlinear equations,
- introduction to numerical integration of function and of differential equations.
Teaching methods
- lectures introducing fundamental methods and concepts of numerical analysis and motivating them through examples and applications,
- exercises sessions in which mathematical problems are analyzed from the numerical point of view,
- computer practice sessions to implement and use Python-based numerical methods in the SciPy ecosystem
- projects to implement mathematical and computer tools for numerical solution of mathematical problems.
Evaluation methods
- a final written exam on theory and exercises for 70% of the final grade, assessing the knowledge and the understanding of the methods and concepts and the ability to apply them, the specific objectives will be provided to students in review questionnaires,
- evaluation of the report and Python code of projects for 30% of the final score, assessing the ability to analyze and numerically solve a mathematical problem.
The projects can only be presented during the term of the course and will therefore have their marks attached to all the sessions of the academic year. The projects are personal works, any participation, either voluntary or by negligence, a plagiarism will be sanctioned.
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
