[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-957873","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Cours acc\u00e9l\u00e9r\u00e9 de g\u00e9om\u00e9trie diff\u00e9rentielle 2025-2026\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          3\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semester 2\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E21\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                                                        \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ELes techniques de base de calcul diff\u00e9rentiel dans les espaces vectoriels r\u00e9els de dimension finie ; les th\u00e9or\u00e8mes d\u0027inversion locale et des fonctions implicites.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ELe but de ce cours est de couvrir les bases de la g\u00e9om\u00e9trie diff\u00e9rentielle en s\u0027appuyant sur la connaissance du calcul diff\u00e9rentiel, avec pour objectif final la cohomologie de de Rham des vari\u00e9t\u00e9s. Pour cela nous introduirons donc les vari\u00e9t\u00e9s, leurs fibr\u00e9s tangents et cotangents, les champs de vecteurs et leurs flots, et les formes diff\u00e9rentielles. Nous verrons alors comment int\u00e9grer ces derni\u00e8res sur les vari\u00e9t\u00e9s, ce qui nous m\u00e8nera naturellement \u00e0 la cohomologie de de Rham et sa c\u00e9l\u00e8bre dualit\u00e9, la dualit\u00e9 de Poincar\u00e9.\u003C\/p\u003E\n\u003Cp\u003EVari\u00e9t\u00e9s diff\u00e9rentielles : espace tangent et cotangent, fonctions lisses\u003Cbr\u003E\nFormes diff\u00e9rentielles : formes exactes et ferm\u00e9es, lemme de Poincar\u00e9.\u003Cbr\u003E\nCohomologie de Rham et applications : quelques calculs, cohomologie des sph\u00e8res\u003Cbr\u003E\nInt\u00e9gration des formes de degr\u00e9 maximum : orientation, vari\u00e9t\u00e9s \u00e0 bord\u003Cbr\u003E\nChamp de vecteurs et formules de Lie-Cartan.\u003C\/p\u003E\n\u003Cp\u003EThe aim of this course is to cover the basis of differential geometry starting from the knowledge of differential calculus, with final aim the de Rham cohomology on manifolds. Differentiable manifolds: tangent and cotangent spaces, smooth functions Differentiable forms: closed and exact forms, Poincar\u00e9\u0027s lemma De Rham cohomology and applications: come computations, cohomology of spheres Integration of maximum degree form: orientation, manifolds with boundary Vector fields and Lie-Cartan formulas.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EJ. Lafontaine, Introduction aux vari\u00e9t\u00e9s diff\u00e9rentielles, Press. Univ. Grenoble, 1996.\u003Cbr\u003E\nF. Paulin, G\u00e9om\u00e9trie diff\u00e9rentielle \u00e9l\u00e9mentaire, Notes de cours, https:\/\/www.imo.universite-paris-saclay.fr\/~paulin\/notescours\/cours_geodiff.pdf\u003Cbr\u003E\nM. Postnikov, Le\u00e7ons de g\u00e9om\u00e9trie : Vari\u00e9t\u00e9s diff\u00e9rentiables, Mir, Moscou, 1990.\u003Cbr\u003E\nM. Spivak, Differential geometry I, Publish or Perish, Wilmington, 1979.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Terminale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]