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| MATH0024-1 | Further Study of Digital Analysis (Equations with Partial Derivatives)
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| Duration : | 30h Th, 30h Pr |
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| Credits/ECTS : |
| civil engineering in electromechanics, 3rd year | | Premier quadrimestre | | 5 |
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| Master in Aerospatial Engineering, in-depth approach, 2nd year | | Premier quadrimestre | | 5 |
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| Master in Computer science, Research Focus, 2nd year | | Premier quadrimestre | | 6 |
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| Master in Engineering Physics, in-depth approach, 1st year | | Premier quadrimestre | | 5 |
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| Master in Engineering Physics, in-depth approach, 2nd year | | Premier quadrimestre | | 5 |
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| Master in Engineering Physics, specialized approach, 1st year | | Premier quadrimestre | | 5 |
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| Master in Engineering Physics, specialized approach, 2nd year | | Premier quadrimestre | | 5 |
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| Holder(s) : | Jean‑André Essers |
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| Language : | Langue française |
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| Course contents : | Classification of partial derivatives.
Theory of characteristics for the hyperbolic systems and associated numerical methods.
Limit conditions; badly-posed questions. Gauchy method. Concept of consistency, convergence and stability of discretisations. Methods of analysing stability. Study of the properties of explicit and implicit diagrams using finite differences to resolve hyperbolic and parabolic systems. Convergence properties of iterative methods used for elliptical equations. |
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| Course objective : | Study of the properties and classification of equation systems of partial derivatives; analysis of properties (precision, stability) of numerical methods using finite differences to resolve them. |
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| Prerequisites : | Basic understanding of partial derivatives and analytical resolution of ordinary differential equations (see course MATH002-0 Mathematical analysis I - Prof. E. DELHEZ). Basic course in numerical analysis (MATH006-0 is required and MATH012-0 is strongly recommended - Prof. F.X. LITT). |
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| Workshops : | Consists of exercise sessions and group work. Exercise sessions will take place in the first semester. The work consists of writing a short calculus programme to resolve certain types of partial derivative equations by using different finite difference diagrams, in groups of 3-4 students. It will take place in the 2nd semester and will be the subject of an oral presentation by the students. It should be noted that every student enrolled for this course is required to carry out this work. The same is true for students who have not carried out this work during the year and present themselves for examination in the 2nd session. |
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| Organization : | During the 1st semester, in line with the timetable. |
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| Written notes : | All handwritten or typed up notes (photocopies). These can be obtained from Prof. J.A. ESSERS's department. |
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| Assessment : | Oral theory exam: 50% - written exercises exam: 30% - group work: 20%. In the first session: written exam in January; oral in January or June. In the second session: written and oral exams in September. |
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| Contacts : | Lecturer: Prof. J.A. ESSERS - Phone 04/366.93.59 -
e-mail JA.Essers@ulg.ac.be
Assistant: Mme I. LEPOT - Phone 04/366.94.39-
e-mail I.Lepot@ulg.ac.be (I.Lepot@ulg.ac.be%20)
Secretary's office: Mme LEROY (Mondays and Fridays) - Phone 04/366.91.36 |
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