Study Programmes 2015-2016
| MATH0464-1 | ||
| Differential geometry II | ||
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Duration :
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| 30h Th, 10h Pr, 20h Mon. WS | ||
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Number of credits :
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Lecturer :
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| 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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Units courses prerequisite and corequisite :
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| Prerequisite or corequisite units are presented within each program | ||
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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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Prerequisite knowledge and skills :
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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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