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| MATH0006-1 | Introduction to numerical analysis
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| Duration : | 30h Th, 30h Pr |
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| Credits/ECTS : |
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| Holder(s) : | Quentin Louveaux |
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| Language : | French language |
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| Course contents : | Numerical analysis is at the boundary between Mathematics and Computer Science. It consists in studying how to practically obtain in a computer different mathematical concepts studied in other courses.
There are two main types of problems studied by numerical analysis:
- how to actually compute results for which an analytical expression exists but that can be obtained more or less accurately depending on the selected method
- how to compute solutions of real problems for which no analytical solution is known but that can be approximated using a computer. |
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| Course objective : | The course is structured in six main chapters (besides the introduction).
Ch 2: Representation of numbers in a computer and roundoff errors
Ch 3: Interpolation and approximation of a known or unknown function.
This is the basis of some of the methods studied in the course.
Ch 4: Solutions of nonlinear equations
Ch 5: Numerical linear algebra
Ch 6: Numerical calculus
Ch 7: Numerical solution of Ordinary Differential Equations |
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| Prerequisites : | An introductory course on linear algebra and calculus. |
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| Workshops : | Seven traditional tutorials are organized.
A programming project in matlab is also organized. This project consists in implementing an exercise based on a real-life problem. The goal of the exercise is to learn to use matlab and to learn to make the good decisions with respect to numerics. |
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| Written notes : | The syllabus is available at the CdC. |
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| Assessment : | The matlab project counts for 25% of the final grade. The exam counts for 75% (in the first as well as in the second session).
The project is evaluated through a short report (5 pages, code in an appendix) and a short oral presentation. An important part of the evaluation consists in the justification of the different choices made in the implementation (in particular on the numerical aspects).
If the obtained note is greater or equal to 10/20, the project cannot be done again. If the note is strictly smaller to 10/20, a new project (with a new problem) can possibly be done for the second session.
The final exam includes a theory part, based on rewriting one proof of the
lecture notes and explainig some concepts, and an exercise part. For this part, no ducuments and no calculators are allowed. It counts for 20% of the final grade. For the second part of the exam, no documents are allowed but a calculator is needed. It consists of exercises and counts for 55% of the final grade. |
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