[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-963144","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  Equations diff\u00e9rentielles et syst\u00e8mes dynamiques\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          5\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemester:\n          Semestre 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\u003ELecture:\u003C\/span\u003E\n                                      \u003Cspan\u003E24\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\u003EDirected study:\u003C\/span\u003E\n                                      \u003Cspan\u003E24\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\u003EFran\u00e7ais\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\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EProbl\u00e8me de Cauchy, solutions globales, solutions maximales ; \u00e9quations d\u2019ordre n, \u00e9quations autonomes ; se ramener \u00e0 ordre 1\/autonome\u003Cbr\u003E\nTh\u00e9or\u00e8me de Cauchy-Lipschitz. Caract\u00e9risation des solutions maximales\u003Cbr\u003E\nLemme de Gronwall. Applications : solutions globales pour les \u00e9quations lin\u00e9aires, ou \u00e0 croissance sous-lin\u00e9aire, d\u00e9pendance continue des solutions par rapport \u00e0 la condition initiale.\u003Cbr\u003E\n\u00c9tude qualitative des \u00e9quations scalaires. R\u00e9gionnement. Comparaison avec une sur ou une sous-solution. Existence de solutions dans un (anti)-entonnoir.\u003Cbr\u003E\n\u00c9quations diff\u00e9rentielles lin\u00e9aires. Rappel sur les \u00e9quations autonomes ; portraits de phase en dimension 2. M\u00e9thode de variation de la constante ; r\u00e9solvante.\u003Cbr\u003E\n\u00c9tude qualitative des \u00e9quations autonomes. Orbites, points stationnaires, portrait de phase, isoclines. \u00c9tude au voisinage d\u2019un point singulier : lin\u00e9aris\u00e9, th\u00e9or\u00e8me de Lyapunov.\u003Cbr\u003E\n\u00c9tude en dimension 2 au voisinage d\u2019un col.\u003Cbr\u003E\n\u00c9tude au voisinage d\u2019un point r\u00e9gulier (admis).\u003Cbr\u003E\nM\u00e9thode d\u2019Euler.\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\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ETh\u00e9orie des \u00e9quations diff\u00e9rentielles ordinaires : EDO lin\u00e9aires, non-lin\u00e9aires : Cauchy-Lipschitz, Gronwall, r\u00e9gularit\u00e9 du flot. Stabilit\u00e9. Etudes qualitatives.\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}]