[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-966311","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  Sciences de l\u0026#039;ing\u00e9nierie et des Syst\u00e8mes\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          Semestre 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\u003E8\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 pratiques :\u003C\/span\u003E\n                                      \u003Cspan\u003E8\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\u003E10\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\u003E1.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Introduction aux m\u00e9thodes num\u00e9riques\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;D\u00e9finition et enjeux des m\u00e9thodes num\u00e9riques.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Erreurs num\u00e9riques : erreur de troncature et erreur d\u2019arrondi.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Notions de convergence et stabilit\u00e9.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Exemples : r\u00e9solution num\u00e9rique de polyn\u00f4mes, calcul d\u2019int\u00e9grales.\u003Cbr\u003E\n2.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;R\u00e9solution num\u00e9rique de syst\u00e8mes d\u2019\u00e9quations statique et dynamiques (EDO)\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thodes ouvertes :\u003Cbr\u003E\no\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thode de Newton-Raphson, m\u00e9thode de la s\u00e9cante.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thodes ferm\u00e9es :\u003Cbr\u003E\no\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thode de bissection, r\u00e9gula falsi.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Crit\u00e8res de convergence.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;R\u00e9solution de syst\u00e8mes lin\u00e9aires :\u003Cbr\u003E\no\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Gauss, Gauss-Seidel, Jacobi.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;R\u00e9solution de syst\u00e8mes non-lin\u00e9aires (Newton multivari\u00e9).\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;R\u00e9solution num\u00e9rique d\u2019EDO : Euler, Runge-Kutta (RK4), m\u00e9thodes implicites.\u003Cbr\u003E\n3.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Interpolation et approximation\u0026nbsp;\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Interpolation polynomiale (Lagrange, Newton).\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Interpolation spline.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Approximation par moindres carr\u00e9s.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Applications : lissage de donn\u00e9es exp\u00e9rimentales.\u003Cbr\u003E\n4.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Optimisation sans contraintes\u0026nbsp;\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Probl\u00e8mes d\u2019optimisation : d\u00e9finition et exemples.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thodes d\u2019optimisation univari\u00e9e :\u003Cbr\u003E\no\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Recherche dichotomique, m\u00e9thode de Newton, m\u00e9thode de la section dor\u00e9e.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thodes multivari\u00e9es :\u003Cbr\u003E\no\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Gradient, gradient conjugu\u00e9, descente de gradient.\u003Cbr\u003E\n5.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Optimisation avec contraintes\u0026nbsp;\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Types de contraintes : \u00e9galit\u00e9s et in\u00e9galit\u00e9s.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thodes classiques :\u003Cbr\u003E\no\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Multiplicateurs de Lagrange.\u003Cbr\u003E\no\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;M\u00e9thodes de p\u00e9nalisation et barri\u00e8re.\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Introduction aux solveurs num\u00e9riques (SciPy, MATLAB fmincon).\u003Cbr\u003E\n6. Applications num\u00e9riques (TP) : Identification des syst\u00e8mes, calcul des points d\u0027\u00e9quilibre, mod\u00e9lisation et approximation des syst\u00e8mes, simulation de syst\u00e8mes (EDO)\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\u003E\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Comprendre les concepts fondamentaux des m\u00e9thodes num\u00e9riques pour r\u00e9soudre des probl\u00e8mes d\u2019ing\u00e9nierie et des syst\u00e8mes.\u0026nbsp;\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Mod\u00e9lisation et simulation des signaux et des syst\u00e8mes dynamiques\u0026nbsp;\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;Savoir formuler et r\u00e9soudre des probl\u00e8mes d\u2019optimisation (univari\u00e9e, multivari\u00e9e, contraintes) pour des applications diverses, notamment, en commande optimale des syst\u00e8mes et en planification de trajectoires\u003Cbr\u003E\n\u2022\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;D\u00e9velopper des comp\u00e9tences pratiques via des travaux dirig\u00e9s (TD) et des travaux pratiques (TP) en Python\/MATLAB.\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\u003E\u2022 Steven Chapra, Raymond Canale, Numerical Mathods for Engineers. Edition 7, McGraw Hill Higher Education, 2014\u003C\/p\u003E\n\u003Cp\u003E\u2022 Gilbert Strang, Computational Science and Engineering, Wellesley-Cambridge Press, 2007\u003C\/p\u003E\n\u003Cp\u003E\u2022 J.-B. Hiriart-Urruty, C. Lemar\u00e9chal, Convex Analysis and Minimization Algorithms, Springer Verlag, 1993\u003C\/p\u003E\n\u003Cp\u003E\u2022 S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press (PDF gratuit).\u003C\/p\u003E\n\u003Cp\u003E\u2022 Nocedal, Wright, Numerical Optimization, Springer, 2006\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}]