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| MATH0464-1 | Differential geometry II
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| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
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| Number of credits : |
| Master in Mathematical Sciences, in-depth approach, 1st year | | 8 |
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| Master in Mathematical Sciences, didactic approach, 1st year | | 8 |
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| Master in Mathematical Sciences, professional focus in management, 1st year | | 8 |
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| Master in Mathematical Sciences, professional focus in computer science, 1st year | | 8 |
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| Master en sciences mathématiques, à finalité spécialisée en statistique, 1st year | | 8 |
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| Master in Mathematical Sciences, specialized approach, 1st year | | 8 |
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| Master in Mathematical Sciences | | 8 |
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| Lecturer : | Pierre Lecomte |
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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 second semester |
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Course contents :
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| Differential equations of order two on manifold and linear connections
On studies the geometrical counter part over a smooth manifold of an ordinary differential equation of order two. Special attention is paid to the case of isochronal equation and their exponential map. This very general concept has many useful particular cases: exponential map of Lie groups, exponential map of matrices, of real or complex numbers, affine maps. It leads to the notion of geodesics. Various charactrizations of a second order differential equation are proposed, among which horizontal distributions on the tangent bundle, the case of linear connection corresponding to isochronal equations that can also be described using covariant derivatives. Flat linear connections are also studied. |
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Learning outcomes of the course :
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Elements of differential geometry. |
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Planned learning activities and teaching methods :
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Mode of delivery (face-to-face ; distance-learning) :
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| Details are given at the beginning of the academic year. |
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Recommended or required readings :
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| A pdf file is avaiable at the http://www.geothalg.ulg.ac.be/GD_Option_I.pdf |
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Assessment methods and criteria :
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| Practical organization to be discussed with the student. |
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| http://www.ulg.ac.be/geothalg
plecomte@ulg.ac.be |
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