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| MATH0251-1 | Analysis III, 1st part
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
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| Lecturer : | Jean-Pierre Schneiders |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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| The first part of the course is devoted to the local theory of systems of non-linear equations (implicit functions, rank theorem, Morse lemma, ...).
The second part contains a detailed study of systems of ordinary differential equations (existence and uniqueness of local and global solutions, special properties of autonomous and linear systems, dependance on initial conditions, ...) |
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Learning outcomes of the course :
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| At the end of the course, the students should have understood completely the results presented during the lectures. They should be able to establish these results and to use them to solve various problems. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| A good understanding of the previous analysis, algebra and geometry courses is essential. |
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Planned learning activities and teaching methods :
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| The course consists of blackboard lessons and exercises sessions.
During the lessons, the main theoretical results are introduced, established and illustrated with examples.
During the exercises sessions, the students are trained to solve by themselves various problems using the results considered in the lessons. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face course |
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Recommended or required readings :
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| Lecture notes are handed out to students at the beginning of the course. |
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Assessment methods and criteria :
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| An examination comprising an oral part on the theory and a written part on the exercices is organized during the first session.
A similar examination is organized during the second session. |
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Work placement(s) :
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Organizational remarks :
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| The course follows the official schedule handed out to the students at the beginning of the academic year. |
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Contacts :
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| Jean-Pierre Schneiders
Département de Mathématique (Build. B37, Office 1/60)
Grande Traverse 12 - 4000 Liège (Sart-Tilman)
Phone : (04) 366.94.01 - E-Mail : jpschneiders@ulg.ac.be
Web page : http://www.analg.ulg.ac.be/jps/ |
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| Items online : |
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| Web page of the course |
| Web page giving access to various informations on the course and to the electronic version of the notes. |
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