[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-968255","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  Analyse Fonctionnelle\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          4\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 1\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\u003E18\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ETravaux dirig\u00e9s :\u003C\/span\u003E\n                                      \u003Cspan\u003E18\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\u003EMetric topology (distance, norm, continuous linear operators, completeness) and integration theory (Lebesgue measure, classical theorems [Fubini, Fatou, Beppo-Levi]; dominated convergence, monotonous convergence).\u003C\/p\u003E\n\u003Cp\u003ENotions de topologie m\u00e9trique (distance, norme, applications lin\u00e9aires continues, compl\u00e9tude) et de calcul int\u00e9gral (mesure de Lebesgue, th\u00e9or\u00e8mes de Fubini, de Fatou, de Beppo-Levi; convergence domin\u00e9e, convergence monotone).\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\u003EEn Fran\u00e7ais :\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EConvexit\u00e9 en dimension infinie.\u003C\/li\u003E\n\u003Cli\u003EDualit\u00e9. Th\u00e9or\u00e8me de repr\u00e9sentation de Riesz pour la dualit\u00e9 Lp.\u003C\/li\u003E\n\u003Cli\u003ETh\u00e9or\u00e8mes de Hahn-Banach.\u003C\/li\u003E\n\u003Cli\u003EBidual topologique.\u003C\/li\u003E\n\u003Cli\u003ECompl\u00e9tude. Th\u00e9or\u00e8me de Baire.\u003C\/li\u003E\n\u003Cli\u003ETh\u00e9or\u00e8mes de Banach (application ouverte, graphe ferm\u00e9, Banach-Alaoglu).\u003C\/li\u003E\n\u003Cli\u003EConvergences faible et *-faible.\u003C\/li\u003E\n\u003Cli\u003EProjection convexe. Minimisation des fonctionnelles semi-continues convexes.\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003EIn English:\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EConvexity in infinite dimension.\u003C\/li\u003E\n\u003Cli\u003EDuality. Riesz representation theorem for duality in Lp.\u003C\/li\u003E\n\u003Cli\u003EHahn-Banach theorems.\u003C\/li\u003E\n\u003Cli\u003ETopological bidual space.\u003C\/li\u003E\n\u003Cli\u003ECompleteness. Baire\u0027s theorem.\u003C\/li\u003E\n\u003Cli\u003EThe Banach theorems (open map, closed graph, Banach-Alaoglu).\u003C\/li\u003E\n\u003Cli\u003EWeak and *-weak convergence.\u003C\/li\u003E\n\u003Cli\u003EConvex projection. Minimization of semi-continuous convex functionals.\u003C\/li\u003E\n\u003C\/ul\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\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EEn Fran\u00e7ais :\u003Cbr\u003E\nComprendre la convexit\u00e9 en dimension infinie et savoir l\u0027appliquer aux formes lin\u00e9aires (continues). Comprendre la compl\u00e9tude en dimension infinie et savoir l\u0027appliquer aux application lin\u00e9aires continues entre espace de Banach. Comprendre les diff\u00e9rents types de convergence.\u003C\/p\u003E\n\u003Cp\u003EIn English:\u003Cbr\u003E\nUnderstand convexity in infinite-dimensional linear spaces and its applications to (continuous) linear forms. Understand completeness in infinite-dimensional linear spaces and its applications to continuous linear maps between Banach spaces. Understand various types of convergence.\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\u003EOrganisation g\u00e9n\u00e9rale et modalit\u00e9s p\u00e9dagogiques\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E18h magistral lectures and 18 h exercises sessions. Final written test (3 h) and shorter test in one exercises session.\u003C\/p\u003E\n\u003Cp\u003E18 h CM et 18 h TD. Examen terminal \u00e9crit de 3 heures. Devoir surveill\u00e9 en TD.\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 Continue non Int\u00e9grale\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}]