{"id":6847,"date":"2023-05-21T10:48:16","date_gmt":"2023-05-21T09:48:16","guid":{"rendered":"http:\/\/www.univ-oeb.dz\/fsesnv\/?page_id=6847"},"modified":"2023-05-21T10:48:16","modified_gmt":"2023-05-21T09:48:16","slug":"nom-du-programme-master-en-mathematiques-appliquees","status":"publish","type":"page","link":"https:\/\/www.univ-oeb.dz\/fsesnv\/nom-du-programme-master-en-mathematiques-appliquees\/","title":{"rendered":"Nom du programme Master en Math\u00e9matiques appliqu\u00e9es\u00a0"},"content":{"rendered":"\n<p class=\"has-medium-font-size\"><strong>D\u00e9partement de Math\u00e9matiques et d&rsquo;Informatique<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-pale-cyan-blue-background-color has-background\"><strong>Nom du programme<\/strong> : Master en Math\u00e9matiques appliqu\u00e9es&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Niveau : <\/strong>Master<\/li>\n\n\n\n<li>Domaine&nbsp;: Math\u00e9matiques et informatique<\/li>\n\n\n\n<li>Fili\u00e8re&nbsp;: Math\u00e9matiques<\/li>\n\n\n\n<li>Sp\u00e9cialit\u00e9&nbsp;: Math\u00e9matiques appliqu\u00e9es&nbsp;<\/li>\n\n\n\n<li>Ann\u00e9e universitaire&nbsp;: 2022\/2023<\/li>\n\n\n\n<li><strong>Description du programme :<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Domaine&nbsp;: Math\u00e9matiques et informatique<\/p>\n\n\n\n<p>Fili\u00e8re&nbsp;: Math\u00e9matiques<\/p>\n\n\n\n<p>Sp\u00e9cialit\u00e9&nbsp;: Math\u00e9matiques appliqu\u00e9es&nbsp;<\/p>\n\n\n\n<p>Ann\u00e9e universitaire&nbsp;: 2022\/2023<\/p>\n\n\n\n<p><strong>Contexte et objectifs de la formation<\/strong><\/p>\n\n\n\n<p><strong>Conditions d\u2019acc\u00e8s&nbsp;: <\/strong>Licence en Math\u00e9matiques<strong> &nbsp;<\/strong><em><\/em><\/p>\n\n\n\n<p><strong>Objectifs de la formation&nbsp;:<\/strong><em><\/em><\/p>\n\n\n\n<p>L&rsquo;objectif du Master mention Math\u00e9matiques appliqu\u00e9es est de fournir aux \u00e9tudiants une formation riche dans des domaines des math\u00e9matiques faisant l&rsquo;objet de recherches actives. Les \u00e9tudiants pourront alors s&rsquo;engager dans la pr\u00e9paration des concours de recrutement&nbsp; de math\u00e9matiques, s&rsquo;orienter vers une activit\u00e9 professionnelle en l&rsquo;industrie, ou pr\u00e9parer une th\u00e8se de math\u00e9matiques pures ou appliqu\u00e9es.<em><\/em><\/p>\n\n\n\n<p>La premi\u00e8re ann\u00e9e du ce master (Master 1) a pour but de familiariser l&rsquo;\u00e9tudiant \u00e0 des outils g\u00e9n\u00e9rales des math\u00e9matiques donc tous les \u00e9tudiants devront obligatoirement suivre tous&nbsp; les cours&nbsp; du semestre 1 et 2. La deuxi\u00e8me ann\u00e9e de master (master 2) permet \u00e0 l&rsquo;\u00e9tudiant d&rsquo;acqu\u00e9rir une formation approfondie &nbsp;dans les domaines d\u2019analyse et des&nbsp; Probabilit\u00e9s et statistique. En semestre 4 il pr\u00e9parera un m\u00e9moire qui sera sanctionn\u00e9 &nbsp;par une soutenance. &nbsp;<\/p>\n\n\n\n<p><strong>Profils et comp\u00e9tences m\u00e9tiers vis\u00e9es<\/strong><strong><\/strong><\/p>\n\n\n\n<p>La formation permet d\u2019acqu\u00e9rir un niveau de connaissances et d\u2019exp\u00e9rience en Math\u00e9matiques suffisant pour, par exemple : se pr\u00e9senter avec de bonnes chances de r\u00e9ussite dans les concours de recrutement, ou commencer une Th\u00e8se de Doctorat. Elle am\u00e8ne donc d\u2019un niveau de Math\u00e9maticien d\u00e9butant (Licence) \u00e0 un niveau de Math\u00e9maticien solide et confirm\u00e9, poss\u00e9dant bien son sujet, et capable de le transmettre ; elle permet aussi, pour ceux qui le souhaitent d\u2019avoir acc\u00e8s \u00e0 des sujets de recherche en d\u00e9veloppement, et \u00e0 des sp\u00e9cialistes de ces sujets, qui les guideront vers le choix d\u2019un travail de Th\u00e8se.<\/p>\n\n\n\n<p><strong>Potentialit\u00e9s r\u00e9gionales et nationales d\u2019employabilit\u00e9 des dipl\u00f4m\u00e9s<\/strong><\/p>\n\n\n\n<p>Les d\u00e9bouch\u00e9s sont les suivants :<\/p>\n\n\n\n<p>\u2022 Le Master permet aux \u00e9tudiants de participer aux concours de recrutement dans les diff\u00e9rents niveaux d\u2019enseignement.<\/p>\n\n\n\n<p>\u2022 Offrir des d\u00e9bouch\u00e9s directs, par exemple vers les recrutements \u00e0 diverses administrations (Compagnes d\u2019assurances, Banques \u2026).<\/p>\n\n\n\n<p>\u2022 ouvrir aux meilleurs \u00e9tudiants le champ de la recherche en math\u00e9matiques pour leur permettre de pr\u00e9parer un Doctorat en math\u00e9matiques dans l\u2019un des laboratoires d\u2019accueil de la Formation Doctorale ou dans un autre laboratoire de Math\u00e9matiques en Alg\u00e9rie ou \u00e0 l\u2019\u00e9tranger.<\/p>\n\n\n\n<p><strong>Passerelles vers les autres sp\u00e9cialit\u00e9s<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Math\u00e9matiques appliqu\u00e9es<\/li>\n\n\n\n<li>Probabilit\u00e9s et statistique.<\/li>\n<\/ul>\n\n\n\n<p><strong>Indicateurs de suivi de la formation&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pour passer du M1 (Master 1) au M2 (Master2) l\u2019\u00e9tudiant devra obtenir 60 Cr\u00e9dits (30 Cr\u00e9dits du semestre 1 et 30 Cr\u00e9dits du semestre 2)<\/li>\n\n\n\n<li>Pour obtenir le dipl\u00f4me final (Master en math\u00e9matiques appliqu\u00e9es) &nbsp;l\u2019\u00e9tudiant devra obtenir 120 Cr\u00e9dits (30 Cr\u00e9dits pour chaque semestre)<\/li>\n\n\n\n<li>Le m\u00e9moire du semestre 4 est sanctionn\u00e9 par une soutenance devant un jury constitu\u00e9&nbsp; de 3 enseignants au moins.<\/li>\n\n\n\n<li>L\u2019\u00e9valuation de l\u2019\u00e9tudiant dans chaque mati\u00e8re sera faite sur la base de deux notes&nbsp;: * la premi\u00e8re est la note du travail continu.&nbsp; * la deuxi\u00e8me est la note de l\u2019examen&nbsp; final en fin du semestre (ou en session de rattrapage en septembre pour les \u00e9tudiants qui n\u2019ont pas obtenu la moyenne 10\/20 dans la mati\u00e8re en question)&nbsp;&nbsp;<\/li>\n<\/ul>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Fiche d\u2019organisation semestrielle des enseignements<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Semestre 1<\/strong><\/li>\n<\/ul>\n\n\n\n<table>\n<tbody>\n<tr>\n<td rowspan=\"2\" width=\"296\"><strong>Unit\u00e9 d\u2019Enseignement<\/strong><\/td>\n<td rowspan=\"2\" width=\"68\"><strong>Coeff<\/strong><\/td>\n<td rowspan=\"2\" width=\"75\"><strong>Cr\u00e9dits<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>Mode d&rsquo;\u00e9valuation<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"86\"><strong>Continu<\/strong><\/td>\n<td width=\"67\"><strong>Examen <\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE fondamentale<\/strong><\/td>\n<td width=\"68\"><strong>9<\/strong><\/td>\n<td width=\"75\"><strong>18<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Compl\u00e9ment de la&nbsp; th\u00e9orie des probabilit\u00e9s<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Analyse fonctionnelle 1<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Compl\u00e9ments sur l&rsquo;int\u00e9gration et les espaces de Lebesgue<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE m\u00e9thodologie<\/strong><\/td>\n<td width=\"68\"><strong>5<\/strong><\/td>\n<td width=\"75\"><strong>9<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">M\u00e9thodes num\u00e9riques<\/td>\n<td width=\"68\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Programmation lin\u00e9aire<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE d\u00e9couverte<\/strong><\/td>\n<td width=\"68\"><strong>2<\/strong><\/td>\n<td width=\"75\"><strong>2<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Anglais<\/td>\n<td width=\"68\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"86\"><em>100%<\/em><\/td>\n<td width=\"67\"><em>&#8211;<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE Transversale<\/strong><\/td>\n<td width=\"68\"><strong>1<\/strong><\/td>\n<td width=\"75\"><strong>1<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Ethique et d\u00e9ontologie du travail<\/td>\n<td width=\"68\"><em><strong>1<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>1<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Semestre<\/strong><strong> &nbsp; 2<\/strong><\/li>\n<\/ul>\n\n\n\n<table>\n<tbody>\n<tr>\n<td rowspan=\"2\" width=\"296\"><strong>Unit\u00e9 d\u2019Enseignement<\/strong><\/td>\n<td rowspan=\"2\" width=\"68\"><strong>Coeff<\/strong><\/td>\n<td rowspan=\"2\" width=\"75\"><strong>Cr\u00e9dits<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>Mode d&rsquo;\u00e9valuation<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"86\"><strong>Continu<\/strong><\/td>\n<td width=\"67\"><strong>Examen <\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE fondamentale<\/strong><\/td>\n<td width=\"68\"><strong>9<\/strong><\/td>\n<td width=\"75\"><strong>18<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Distributions 1<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Analyse fonctionnelle 2<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Statistique inf\u00e9rentielle<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE m\u00e9thodologie<\/strong><\/td>\n<td width=\"68\"><strong>5<\/strong><\/td>\n<td width=\"75\"><strong>9<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Optimisation avec contraintes<\/td>\n<td width=\"68\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Equations aux d\u00e9riv\u00e9s&nbsp; partielles<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE d\u00e9couverte<\/strong><\/td>\n<td width=\"68\"><strong>2<\/strong><\/td>\n<td width=\"75\"><strong>2<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Latex<\/td>\n<td width=\"68\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"86\"><em>100%<\/em><\/td>\n<td width=\"67\"><em>&#8211;<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE Transversale<\/strong><\/td>\n<td width=\"68\"><strong>1<\/strong><\/td>\n<td width=\"75\"><strong>1<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>Thinking skills<\/strong><\/td>\n<td width=\"68\"><em><strong>1<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>1<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Semestre<\/strong><strong> &nbsp; 3<\/strong><\/li>\n<\/ul>\n\n\n\n<table>\n<tbody>\n<tr>\n<td rowspan=\"2\" width=\"296\"><strong>Unit\u00e9 d\u2019Enseignement<\/strong><\/td>\n<td rowspan=\"2\" width=\"68\"><strong>Coeff<\/strong><\/td>\n<td rowspan=\"2\" width=\"75\"><strong>Cr\u00e9dits<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>Mode d&rsquo;\u00e9valuation<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"86\"><strong>Continu<\/strong><\/td>\n<td width=\"67\"><strong>Examen<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE fondamentale<\/strong><\/td>\n<td width=\"68\"><strong>9<\/strong><\/td>\n<td width=\"75\"><strong>18<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Distributions 2<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Th\u00e9orie variationnelle&nbsp; des \u00e9quations elliptiques<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Processus al\u00e9atoires et fiabilit\u00e9 des syst\u00e8mes<\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE m\u00e9thodologie<\/strong><\/td>\n<td width=\"68\"><strong>5<\/strong><\/td>\n<td width=\"75\"><strong>9<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">Th\u00e9orie&nbsp; du&nbsp; contr\u00f4le<\/td>\n<td width=\"68\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><a href=\"https:\/\/www.google.dz\/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=8&amp;cad=rja&amp;uact=8&amp;ved=0ahUKEwjwv6rejLTKAhWHW5AKHZzEDeEQFghVMAc&amp;url=http%3A%2F%2Fwww.lps.ens.fr%2F%7Evincent%2Fch1e.pdf&amp;usg=AFQjCNFjWsvQAHrt4J1E6pJCAUhUKKeocg&amp;bvm=bv.112064104,d.bGQ\">Syst\u00e8mes dynamiques et introduction au chaos<\/a><\/td>\n<td width=\"68\"><em><strong>3<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>6<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE d\u00e9couverte<\/strong><\/td>\n<td width=\"68\"><strong>2<\/strong><\/td>\n<td width=\"75\"><strong>2<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">S\u00e9minaires<\/td>\n<td width=\"68\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>2<\/strong><\/em><\/td>\n<td width=\"86\"><em>100%<\/em><\/td>\n<td width=\"67\"><em>&#8211;<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"296\"><strong>UE Transversale<\/strong><\/td>\n<td width=\"68\"><strong>1<\/strong><\/td>\n<td width=\"75\"><strong>1<\/strong><\/td>\n<td colspan=\"2\" width=\"153\"><strong>&nbsp;<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"296\">R\u00e9daction scientifique<\/td>\n<td width=\"68\"><em><strong>1<\/strong><\/em><\/td>\n<td width=\"75\"><em><strong>1<\/strong><\/em><\/td>\n<td width=\"86\"><em>50%<\/em><\/td>\n<td width=\"67\"><em>50%<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Semestre 4&nbsp;<\/strong><strong><\/strong><\/li>\n<\/ul>\n\n\n\n<p>Le semestre 4 est consacr\u00e9 \u00e0 un m\u00e9moire sanctionn\u00e9 par une soutenance.<strong><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>&nbsp;<\/strong><\/td><td><strong>VHS<\/strong><\/td><td><strong>Coeff<\/strong><\/td><td><strong>Cr\u00e9dits<\/strong><\/td><\/tr><tr><td><strong>Travail Personnel<\/strong><\/td><td>675h<\/td><td>15<\/td><td>30<\/td><\/tr><tr><td><strong>Stage en entreprise<\/strong><\/td><td>00<\/td><td>00<\/td><td>00<\/td><\/tr><tr><td><strong>S\u00e9minaires<\/strong><\/td><td>00<\/td><td>00<\/td><td>00<\/td><\/tr><tr><td><strong>Autre (pr\u00e9ciser)<\/strong><\/td><td>00<\/td><td>00<\/td><td>00<\/td><\/tr><tr><td><strong>Total Semestre 4<\/strong><\/td><td>675h<\/td><td>15<\/td><td>30<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Programme d\u00e9taill\u00e9 par mati\u00e8re<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;: Math\u00e9matiques appliqu\u00e9es&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;: S1<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de l\u2019UE&nbsp;: Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re&nbsp;: Compl\u00e9ment de la&nbsp; th\u00e9orie des probabilit\u00e9s<\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits&nbsp;: 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficients&nbsp;: 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong><\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de compl\u00e9ter leurs connaissances en th\u00e9orie des probabilit\u00e9s.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res de probabilit\u00e9&nbsp; et de la th\u00e9orie de la mesure de la licence de math\u00e9matiques fondamentales.<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1<\/strong>&nbsp;: Vecteurs al\u00e9atoires<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Lois de probabilit\u00e9 d\u2019un vecteur al\u00e9atoire<\/li>\n\n\n\n<li>Matrice de covariance<\/li>\n\n\n\n<li>In\u00e9galit\u00e9s sur les variables al\u00e9atoires (Markov, &nbsp;Bienayme- Chebishev&nbsp; et autres \u2026)&nbsp;<\/li>\n\n\n\n<li>Ind\u00e9pendance des variables al\u00e9atoires&nbsp;<\/li>\n\n\n\n<li>Vecteurs al\u00e9atoires Gaussiens.<\/li>\n\n\n\n<li>Esp\u00e9rance conditionnelle<\/li>\n<\/ul>\n\n\n\n<p><strong>Chapitre 2<\/strong>&nbsp;: Convergence des suites de v. a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Convergence en loi<\/li>\n\n\n\n<li>Convergence presque sure<\/li>\n\n\n\n<li>Convergence en probabilit\u00e9.<\/li>\n\n\n\n<li>Convergence en moyenne d\u2019ordre p.<\/li>\n<\/ul>\n\n\n\n<p><strong>Chapitre 3<\/strong>&nbsp;: Fonctions caract\u00e9ristiques et fonctions g\u00e9n\u00e9ratrices.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<strong>I-<\/strong>&nbsp;&nbsp; Fonctions caract\u00e9ristiques<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &#8211; Fonction caract\u00e9ristique de la somme de v.a ind\u00e9pendantes<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &#8211; Formule d\u2019inversion<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &#8211; Fonction caract\u00e9ristique et moments.<\/p>\n\n\n\n<p>&nbsp; &nbsp;<strong>II-<\/strong> Fonctions g\u00e9n\u00e9ratrices<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &#8211; Fonction g\u00e9n\u00e9ratrice de la somme de v.a ind\u00e9pendantes<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &#8211; Fonction g\u00e9n\u00e9ratrice et moments.<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>40% travail continu et 60%&nbsp; Examen<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites internet, etc.).<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li>M. M\u00e9tivier, \u00ab&nbsp;Notions fondamentales de la th\u00e9orie des probabilit\u00e9s&nbsp;\u00bb 2eme \u00e9dition DUNOD Paris 1972.<\/li>\n\n\n\n<li>JP Ansel et Y. Ducel,&nbsp; \u00ab&nbsp;Exercices corrig\u00e9s en th\u00e9orie des probabilit\u00e9s&nbsp;\u00bb 2 cycle universitaire ellipses.<\/li>\n\n\n\n<li>M Cottrell et al , \u00abexercices de probabilit\u00e9s&nbsp;\u00bb licence, master, \u00e9coles d\u2019ing\u00e9nieurs. CASSINI.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S1&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re&nbsp;:&nbsp;&nbsp;&nbsp; Analyse fonctionnelle 1<\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits : 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement : <\/strong>Ce cours de Master pr\u00e9sente les bases de l&rsquo;Analyse fonctionnelle lin\u00e9aire sous une forme sensiblement plus \u00e9labor\u00e9e que celle du niveau d&rsquo;un cours de Licence. Tout en restant dans des limites raisonnables, on a cherch\u00e9 \u00e0 donner le panorama le plus large possible \u00e0 ce niveau. Ceci permettra aux \u00e9tudiants de compl\u00e9ter et d&rsquo;approfondir leurs connaissances en analyse fonctionnelle. L&rsquo;accent est mis sur les aspects \u00ab\u00a0abstraits\u00a0\u00bbutiles tant aux \u00e9tudiants int\u00e9ress\u00e9s par les \u00ab\u00a0Math\u00e9matiques Pures\u00a0\u00bb qu&rsquo;\u00e0 ceux qui d\u00e9sirent s&rsquo;orienter vers les \u00ab\u00a0Math\u00e9matiques appliqu\u00e9es\u00a0\u00bb.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es : <\/strong>Alg\u00e8bre 2, Introduction \u00e0 la topologie.<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re :<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1.&nbsp;&nbsp;&nbsp; Espaces de Banach<\/strong><\/p>\n\n\n\n<p>1.1 Espaces vectoriels norm\u00e9s<\/p>\n\n\n\n<p>1.2 Espaces de Banach<\/p>\n\n\n\n<p>1.3 Etude de quelques exemples fondamentaux :<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.3.1 Espaces de fonctions born\u00e9es et sous-espaces remarquables .<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.3.2 Espaces de fonctions r\u00e9guli\u00e8res.<\/p>\n\n\n\n<p>1.4 Espaces de fonctions continues .<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.4.1 Convergence simple et convergence uniforme d&rsquo;une suite de fonctions<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.4.2 Equicontinuit\u00e9 et th\u00e9or\u00e8me de compacit\u00e9 d&rsquo;Ascoli-Arzel\u00e0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.4.3 Th\u00e9or\u00e8me d&rsquo;approximation de Stone-Weierstrass et applications<\/p>\n\n\n\n<p><strong>Chapitre 2.&nbsp;&nbsp;&nbsp; Th\u00e9orie des op\u00e9rateurs lin\u00e9aires : Concepts et r\u00e9sultats de base<\/strong><\/p>\n\n\n\n<p>2.1 Terminologie de base de la th\u00e9orie des op\u00e9rateurs<\/p>\n\n\n\n<p>2.2 Op\u00e9rateurs lin\u00e9aires continus, op\u00e9rateurs lin\u00e9aires born\u00e9s<\/p>\n\n\n\n<p>2.3 Espace des op\u00e9rateurs lin\u00e9aires born\u00e9s :<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2.4 Quelques propri\u00e9t\u00e9s fondamentales des op\u00e9rateurs lin\u00e9aires born\u00e9s :<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2.4.1 Th\u00e9or\u00e8me de Banach-Steinhaus et ses cons\u00e9quences,<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2.4.2 Th\u00e9or\u00e8me de l&rsquo;application ouvertes et du graphe ferm\u00e9.<\/p>\n\n\n\n<p>2.5 Op\u00e9rateurs inverses et applications \u00e0 la r\u00e9solution de l&rsquo;\u00e9quation.<\/p>\n\n\n\n<p>2.6 Introduction \u00e0 la th\u00e9orie spectrale des op\u00e9rateurs lin\u00e9aires<\/p>\n\n\n\n<p>2.7 Op\u00e9rateurs ferm\u00e9s et application aux \u00e9quations diff\u00e9rentielles.<\/p>\n\n\n\n<p><strong>Chapitre 3.&nbsp;&nbsp; Dualit\u00e9 et op\u00e9rateurs adjoints<\/strong><\/p>\n\n\n\n<p>3.1 Dual d&rsquo;un espace norm\u00e9, exemples fondamentaux .<\/p>\n\n\n\n<p>3.2 Th\u00e9or\u00e8me de Hahn-Banach et ses corollaires<\/p>\n\n\n\n<p>3.3 Bidual, espaces r\u00e9flexifs<\/p>\n\n\n\n<p>3.4 Convergence faible et compacit\u00e9 faible<\/p>\n\n\n\n<p>3.5 Op\u00e9rateur adjoint (transpos\u00e9) d&rsquo;un op\u00e9rateur lin\u00e9aire born\u00e9<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation: <\/strong><strong>Contr\u00f4le continu (40%), Examen (60%)<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences<\/strong>:<\/p>\n\n\n\n<p>1. V. Hutson, J.S. Pym and M.J. Cloud, Applications of Functional Analysis and Operator Theory, Elsevier Science, 2005.<\/p>\n\n\n\n<p>2. V. Tr\u00e9noguine, Analyse Fonctionnelle, Editions Mir, 1985.<\/p>\n\n\n\n<p>3. H. Brezis, Analyse Fonctionnelle Th\u00e9orie et Applications, Dunod, 2005<\/p>\n\n\n\n<p>4. A. Bressan, Lecture Notes on Functional Analysis With Applications to Linear Partial Differential Equations, American Mathematical Society, 2012<\/p>\n\n\n\n<p>5. B. Rynne, M.A. Youngson, Linear Functional Analysis, Springer, 2008<\/p>\n\n\n\n<p>6. E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley &amp; Sons, 1978.<\/p>\n\n\n\n<p>7. N. El Hage Hassan, Topologie g\u00e9n\u00e9rale et Espaces norm\u00e9s, Dunod, 2011.<\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S1&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re&nbsp;:&nbsp;&nbsp; <\/strong><strong>Compl\u00e9ments sur l&rsquo;int\u00e9gration et les espaces de Lebesgue<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : <\/strong><strong>Fondamentale<\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits : 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong><\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de compl\u00e9ter leurs connaissances en th\u00e9orie de l\u2019int\u00e9gration.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis la mati\u00e8re de la th\u00e9orie de la mesure et int\u00e9gration de la licence de math\u00e9matiques fondamentales&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1: L&rsquo;int\u00e9grale de Lebesgue sur R<sup>n<\/sup><\/strong><\/p>\n\n\n\n<p>1. Rappels et compl\u00e9ments sur la mesure et l\u2019int\u00e9grale de Lebesgue sur R.<\/p>\n\n\n\n<p>2. Produit fini d&rsquo;espaces mesur\u00e9s.<\/p>\n\n\n\n<p>2. Application : Mesure de Lebesgue sur la tribu B<sub>n<\/sub> des bor\u00e9liens de R<sup>n<\/sup> et l&rsquo;int\u00e9grale de<\/p>\n\n\n\n<p>Lebesgue sur R<sup>n<\/sup><\/p>\n\n\n\n<p>3. Th\u00e9or\u00e8me de Fubini-Tonelli et th\u00e9or\u00e8me de Fubini<\/p>\n\n\n\n<p>4. Application au calcul des int\u00e9grales multiples et formule de changement de variables<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>40% travail continu et 60%&nbsp; Examen<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites Internet, etc.).<\/p>\n\n\n\n<p>1. P. BILLINGSLEY (1968) Convergence of Probability measures Wiley<\/p>\n\n\n\n<p>2. P. R. HALMOS (1950) Measure Theory Van Nostrand.<\/p>\n\n\n\n<p>3. Roger Jean Mesure et int\u00e9gration<\/p>\n\n\n\n<p>4. Jean Christofe Breton Int\u00e9grale de Lebesgue Universit\u00e9&nbsp; de Renne 1 (on line).<\/p>\n\n\n\n<p>5- R. Dautray, J-L. Lions, Analyse math\u00e9matique et calcul num\u00e9rique pour les sciences et les techniques, Vol. 8, Masson, Paris, 1984.<\/p>\n\n\n\n<p>6- J. Droniou, Int\u00e9gration et espaces de Sobolev \u00e0 valeurs vectorielles, Polycopi\u00e9 de l&rsquo;\u00e9cole<\/p>\n\n\n\n<p>doctorale de Math-Info \u00e0 Marseille, 2001. Disponible depuis l&rsquo;adresse :<\/p>\n\n\n\n<p>http:\/\/www-gm3.univ-mrs.fr\/polys<\/p>\n\n\n\n<p>7- H. Brezis, Op\u00e9rateurs maximaux monotones et semi-groupes de contraction, North-Holland Publishing Company, 1973.<\/p>\n\n\n\n<p>8-H. Brezis, Analyse Fonctionnelle Th\u00e9orie et Applications, Dunod, 2005<\/p>\n\n\n\n<p>9-E.H. Lieb, M. Loss, Analysis, American Mathematical Society, 2001<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S1&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re&nbsp;:&nbsp;&nbsp;&nbsp; M\u00e9thodes num\u00e9riques<\/strong> <strong><\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : M\u00e9thodologie<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits : 5<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 2<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong>.&nbsp;&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de compl\u00e9ter leurs connaissances sur les m\u00e9thodes de l\u2019analyse num\u00e9riques.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis la mati\u00e8re d\u2019analyse num\u00e9rique de la licence de math\u00e9matiques fondamentales.<\/p>\n\n\n\n<p><strong>Chapitre 1.<\/strong><\/p>\n\n\n\n<p>M\u00e9thodes num\u00e9riques pour les \u00e9quations diff\u00e9rentielles.<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li>M\u00e9thodes \u00e0 un pas.<\/li>\n\n\n\n<li>M\u00e9thodes \u00e0 pas multiples.<\/li>\n<\/ol>\n\n\n\n<p><strong>Chapitre 2.<\/strong><\/p>\n\n\n\n<p>Formulation variationnelle.<\/p>\n\n\n\n<p>1) Le probl\u00e8me de Poisson en 1D.<\/p>\n\n\n\n<p>2) Conditions aux limites de Neumann.<\/p>\n\n\n\n<p>3) Le probl\u00e8me de la Poisson&nbsp; en 2D.<\/p>\n\n\n\n<p><strong>Chapitre 3.<\/strong><\/p>\n\n\n\n<p>Calcul de solutions approch\u00e9es par la m\u00e9thode des \u00e9l\u00e9ments finis<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li>La m\u00e9thode de Galerkin.<\/li>\n\n\n\n<li>La m\u00e9thode des \u00e9l\u00e9ments finis.<\/li>\n\n\n\n<li>La m\u00e9thode des \u00e9l\u00e9ments finis en 1D.<\/li>\n\n\n\n<li>La m\u00e9thode des \u00e9l\u00e9ments finis en 2D.<\/li>\n<\/ol>\n\n\n\n<p><strong>Chapitre 4.<\/strong><\/p>\n\n\n\n<p>Analyse d\u2019erreur.<\/p>\n\n\n\n<p>Erreurs de discr\u00e9tisation et d\u2019interpolation.<\/p>\n\n\n\n<p>Erreur d\u2019interpolation en dimension 1.<\/p>\n\n\n\n<p>Super convergence.<\/p>\n\n\n\n<p><strong>Bibliographie.<\/strong><\/p>\n\n\n\n[1] H. Brezis, Analyse Fonctionnelle&nbsp;: Th\u00e9orie et Applications (Masson, Paris). 1983.<\/p>\n\n\n\n[2] P. G. Ciarlet, Introduction \u00e0 l\u2019analyse num\u00e9rique et \u00e0 l\u2019optimisation, Masson 1982.<\/p>\n\n\n\n[3] R. Eymard, T. Gallou\u00e9t and R. Herbin, Finite Volume Methods, Handbook of Numerical Analysis, Vol. VII, pp. 713-1020. Edited by P. G. Ciarlet and J. L. Lions (North Holland). Version en ligne &nbsp;http:\/\/www.cmi.univ-mrs.fr\/herbin\/PUBLI\/bookevol.pdf<\/p>\n\n\n\n[4] T. Gallou\u00e9t and R. Herbin, Mesures, Int\u00e9gration, Probabilit\u00e9s.<\/p>\n\n\n\n<p>http :\/\/www.cmi.univmrs.fr\/ gallouet\/licence.d\/mes-int-pro.pdf<\/p>\n\n\n\n[5] R. Herbin, Analyse num\u00e9rique. &nbsp;http:\/\/www.cmi.univ-mrs.fr\/herbin\/PUBLI\/anamat.pdf<\/p>\n\n\n\n[6] J. RAPPAZ AND M. PICASSO, Introduction \u00e0 l\u2019analyse num\u00e9rique. Presses Polytechniques et Universitaires Romandes, Lausanne, 1998.<\/p>\n\n\n\n[7] P. A. RAVIART AND JM THOMAS, Introduction \u00e0 l\u2019analyse num\u00e9rique des \u00e9quations aux d\u00e9riv\u00e9es partielles.<\/p>\n\n\n\n[8] Rapha\u00e8le Herbin, Universit\u00e9 Aix Marseille 1, Master de math\u00e9matiques, Analyse num\u00e9rique des \u00e9quations aux d\u00e9riv\u00e9es partielles, 13 d\u00e9cembre 2012.<\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S1&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re&nbsp;:&nbsp;&nbsp;&nbsp; Programmation lin\u00e9aire<\/strong> <strong><\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : M\u00e9thodologie<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits : 4<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 2<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement :<\/strong><\/p>\n\n\n\n<p>Ce module a pour objectifs de sensibiliser l&rsquo;\u00e9tudiant \u00e0 l&rsquo;importance pratique des probl\u00e8mes<\/p>\n\n\n\n<p>d\u2019optimisation lin\u00e9aires, de ma\u00eetriser l\u2019ensemble th\u00e9orique sous-jacent, et de pouvoir utiliser ces<\/p>\n\n\n\n<p>techniques dans des probl\u00e8mes pratiques.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es : <\/strong>Math\u00e9matiques et informatique g\u00e9n\u00e9rales<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re :<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1 : Introduction g\u00e9n\u00e9rale<\/strong><\/p>\n\n\n\n<p>1.1 Historique de la programmation lin\u00e9aire<\/p>\n\n\n\n<p>1.2 Exemples de mod\u00e9lisation de probl\u00e8mes pratiques sous forme de programme lin\u00e9aire.<\/p>\n\n\n\n<p><strong>Chapitre 2 : G\u00e9om\u00e9trie de la programmation lin\u00e9aire<\/strong><\/p>\n\n\n\n<p>2.1 Espaces vectoriels, rang de matrice, syst\u00e8mes d\u2019\u00e9quations lin\u00e9aires<\/p>\n\n\n\n<p>2.2 Ensemble convexe, hyperplan, poly\u00e8dre, simplexe, point extr\u00eame<\/p>\n\n\n\n<p><strong>Chapitre 3 : M\u00e9thode primale de r\u00e9solution d\u2019un programme lin\u00e9aire<\/strong><\/p>\n\n\n\n<p>3.1 Position du probl\u00e8me<\/p>\n\n\n\n<p>3.2 Caract\u00e9risation des points extr\u00eames<\/p>\n\n\n\n<p>3.3 Optimalit\u00e9 en un point extr\u00eame<\/p>\n\n\n\n<p>3.4 Crit\u00e8res d\u2019optimalit\u00e9 : formule d\u2019accroissement de la fonction objectif, crit\u00e8re d\u2019optimalit\u00e9, 3.5<\/p>\n\n\n\n<p>condition suffisante d\u2019existence de solution non born\u00e9e<\/p>\n\n\n\n<p>3.6 Algorithme du simplexe : am\u00e9lioration de la fonction objectif en passant d\u2019un pont extr\u00eame \u00e0 un<\/p>\n\n\n\n<p>autre, algorithme du simplexe sous forme matricielle, finitude de l\u2019algorithme du simplexe,<\/p>\n\n\n\n<p>algorithme et tableau du simplexe<\/p>\n\n\n\n<p>3.7 Initiation de l\u2019algorithme du simplexe : cas du programme lin\u00e9aire sous forme normale, Mm\u00e9thode,<\/p>\n\n\n\n<p>m\u00e9thode de deux phases,<\/p>\n\n\n\n<p><strong>Chapitre 4 : M\u00e9thodes duales en programmation lin\u00e9aire<\/strong><\/p>\n\n\n\n<p>4.1 D\u00e9finitions<\/p>\n\n\n\n<p>4.2 Formule d\u2019accroissement de la fonction duale et crit\u00e8re d\u2019optimalit\u00e9<\/p>\n\n\n\n<p>4.3 Condition suffisante de solutions r\u00e9alisables dans le probl\u00e8me primale<\/p>\n\n\n\n<p>4.4 Algorithme dual du simplexe<\/p>\n\n\n\n<p>Initialisation de l\u2019algorithme duale du simplexe<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation : Examen (60%) , contr\u00f4le continu (40%)<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences<\/strong>:<\/p>\n\n\n\n<p>1. M. Sakarovicth, Graphes et programmation lin\u00e9aire, Ed. Hermann. 1984.<\/p>\n\n\n\n<p>2. H. Mauran, Programmation lin\u00e9aire appliqu\u00e9e, Ed. Technip, 1967.<\/p>\n\n\n\n<p>3. A. Kauffman, M\u00e9thodes et mod\u00e8les de R.O., Ed. Dunod, 1976.<\/p>\n\n\n\n<p>4. V. Chvatal, Linear programming. W.H. Freeman and Company, 1983.<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S1&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re&nbsp;:&nbsp;&nbsp; Anglais <\/strong>&nbsp;<strong><\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : D\u00e9couverte<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 1<\/strong> <strong><\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong> (D\u00e9crire ce que l\u2019\u00e9tudiant est cens\u00e9 avoir acquis comme comp\u00e9tences apr\u00e8s le succ\u00e8s \u00e0 cette mati\u00e8re \u2013 maximum 3 lignes).&nbsp;&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; d\u2019am\u00e9liorer leurs niveaux&nbsp; en anglais&nbsp;&nbsp; .<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es (<\/strong>descriptif succinct des connaissances requises pour pouvoir suivre cet enseignement \u2013 Maximum 2 lignes).&nbsp;<\/p>\n\n\n\n<p>&nbsp;Anglais de base<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:&nbsp;<\/strong><\/p>\n\n\n\n<p>Anglais scientifiques<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>100%&nbsp; Examen<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites Internet, etc.).<\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es <\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S1&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de l\u2019UE&nbsp;: Transversale<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re: Ethique et d\u00e9ontologie du travail<\/strong><\/p>\n\n\n\n<p><strong>Coefficients&nbsp;: 1<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits&nbsp;: 1<\/strong><\/p>\n\n\n\n<p><strong>\u0627\u0644\u0647\u062f\u0641 \u0645\u0646 \u0627\u0644\u0645\u0627\u062f\u0629:<\/strong><\/p>\n\n\n\n<p>\u062a\u0648\u0639\u064a\u0629 \u0627\u0644\u0637\u0627\u0644\u0628 \u0648\u062a\u062d\u0633\u064a\u0633\u0647 \u0645\u0646 \u062e\u0637\u0631 \u0627\u0644\u0641\u0633\u0627\u062f \u0648\u062f\u0641\u0639\u0647 \u0644\u0644\u0645\u0633\u0627\u0647\u0645\u0629 \u0641\u064a \u0645\u062d\u0627\u0631\u0628\u062a\u0647.<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li>\u062c\u0648\u0647\u0631 \u0627\u0644\u0641\u0633\u0627\u062f<\/li>\n\n\n\n<li>\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0641\u0633\u0627\u062f<\/li>\n\n\n\n<li>\u0645\u0638\u0627\u0647\u0631 \u0627\u0644\u0641\u0633\u0627\u062f \u0627\u0644\u0625\u062f\u0627\u0631\u064a \u0648\u0627\u0644\u0645\u0627\u0644\u064a<\/li>\n\n\n\n<li>\u0623\u0633\u0628\u0627\u0628 \u0627\u0644\u0641\u0633\u0627\u062f \u0627\u0644\u0625\u062f\u0627\u0631\u064a \u0648\u0627\u0644\u0645\u0627\u0644\u064a&nbsp;<\/li>\n\n\n\n<li>\u0622\u062b\u0627\u0631 \u0627\u0644\u0641\u0633\u0627\u062f \u0627\u0644\u0625\u062f\u0627\u0631\u064a \u0648\u0627\u0644\u0645\u0627\u0644\u064a<\/li>\n\n\n\n<li>\u0645\u062d\u0627\u0631\u0628\u0629 \u0627\u0644\u0641\u0633\u0627\u062f \u0645\u0646 \u0637\u0631\u0641 \u0627\u0644\u0647\u064a\u0626\u0627\u062a \u0648\u0627\u0644\u0645\u0646\u0638\u0645\u0627\u062a \u0627\u0644\u062f\u0648\u0644\u064a\u0629 \u0648\u0627\u0644\u0645\u062d\u0644\u064a\u0629<\/li>\n\n\n\n<li>\u0637\u0631\u0642 \u0627\u0644\u0639\u0644\u0627\u062c \u0648\u0633\u0628\u0644 \u0645\u062d\u0627\u0631\u0628\u0629 \u0638\u0627\u0647\u0631\u0629 \u0627\u0644\u0641\u0633\u0627\u062f<\/li>\n\n\n\n<li>\u0646\u0645\u0627\u0630\u062c \u0644\u062a\u062c\u0627\u0631\u0628 \u0628\u0639\u0636 \u0627\u0644\u062f\u0648\u0644 \u0641\u064a \u0645\u0643\u0627\u0641\u062d\u0629 \u0627\u0644\u0641\u0633\u0627\u062f<strong><\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>100% Examen<\/p>\n\n\n\n<p><strong>\u0627\u0644\u0645\u0631\u0627\u062c\u0639:<\/strong><\/p>\n\n\n\n<p>\u0645\u0648\u0633\u0649 , \u0635\u0627\u0641\u064a \u0625\u0645\u0627\u0645 . ( 1405 \u0647\u0640 \/ 1985 \u0645 ) . <strong>\u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0627\u0644\u0625\u0635\u0644\u0627\u062d \u0627\u0644\u0625\u062f\u0627\u0631\u064a \u0648\u0625\u0639\u0627\u062f\u0629 \u0627\u0644\u062a\u0646\u0638\u064a\u0645 \u0641\u064a \u0646\u0637\u0627\u0642 \u0627\u0644\u0641\u0643\u0631 \u0648\u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a<\/strong> ( \u06371 ) . \u0627\u0644\u0631\u064a\u0627\u0636 : \u062f\u0627\u0631 \u0627\u0644\u0639\u0644\u0648\u0645 \u0644\u0644\u0637\u0628\u0627\u0639\u0629 \u0648\u0627\u0644\u0646\u0634\u0631 .<\/p>\n\n\n\n<p><a href=\"http:\/\/www.islameiat.com\/doc\/article.php?sid=276&amp;mode=&amp;order=0\">http:\/\/www.islameiat.com\/doc\/article.php?sid=276&amp;mode=&amp;order=0<\/a><\/p>\n\n\n\n<p>\u0628\u062d\u0631 , \u064a\u0648\u0633\u0641 . <strong>\u0627\u0644\u0641\u0633\u0627\u062f \u0627\u0644\u0625\u062f\u0627\u0631\u064a \u0648\u0645\u0639\u0627\u0644\u062c\u062a\u0647 \u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0625\u0633\u0644\u0627\u0645\u064a<\/strong><\/p>\n\n\n\n<p><a href=\"http:\/\/www.scc-online.net\/thaqafa\/th_1.htm\">http:\/\/www.scc-online.net\/thaqafa\/th_1.htm<\/a><\/p>\n\n\n\n<p>\u062d\u0645\u0648\u062f\u064a , \u0647\u0645\u0627\u0645 . <strong>\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u0641\u0633\u0627\u062f \u0641\u064a \u0627\u0644\u0642\u0631\u0622\u0646 \u0627\u0644\u0643\u0631\u064a\u0645<\/strong> .<\/p>\n\n\n\n<p><a href=\"http:\/\/209.61.210.137\/uofislam\/behoth\/behoth_quran\/16\/a1.htm\">http:\/\/209.61.210.137\/uofislam\/behoth\/behoth_quran\/16\/a1.htm<\/a><\/p>\n\n\n\n<p>\u0627\u0644\u0641\u0642\u064a , \u0645\u0635\u0637\u0641\u0649. <strong>\u0627\u0644\u0641\u0633\u0627\u062f \u0627\u0644\u0625\u062f\u0627\u0631\u064a \u0648\u0627\u0644\u0645\u0627\u0644\u064a \u0628\u064a\u0646 \u0627\u0644\u0633\u064a\u0627\u0633\u0627\u062a \u0648\u0627\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a<\/strong><\/p>\n\n\n\n<p><a href=\"http:\/\/www.cipe-egypt.org\/articles\/art0900.htm\">http:\/\/www.cipe-egypt.org\/articles\/art0900.htm<\/a><\/p>\n\n\n\n<p>\u0645\u062d\u0645\u0648\u062f , \u0645\u0647\u064a\u0648\u0628 \u062e\u0636\u0631<strong> . \u0645\u0646 \u0645\u0639\u0627\u0644\u0645 \u0627\u0644\u0645\u062f\u0631\u0633\u0629 \u0627\u0644\u0639\u0645\u0631\u064a\u0629 \u0641\u064a \u0645\u0643\u0627\u0641\u062d\u0629 \u0627\u0644\u0641\u0633\u0627\u062f<\/strong> .<\/p>\n\n\n\n<p><a href=\"http:\/\/www.hetta.com\/current\/mahyoob23.htm\">http:\/\/www.hetta.com\/current\/mahyoob23.htm<\/a><\/p>\n\n\n\n<p>\u0628\u0632\u0627\u0632 , \u0633\u0639\u062f <strong>&nbsp;. \u062d\u0645\u0644\u0629 \u0636\u062f \u0627\u0644\u0641\u0633\u0627\u062f<\/strong><\/p>\n\n\n\n<p><a href=\"http:\/\/www.saadbazzaz.com\/index.asp?fname=articles%5C7540.htm&amp;code=display\">http:\/\/www.saadbazzaz.com\/index.asp?fname=articles%5C7540.htm&amp;code=display<\/a><strong><\/strong><\/p>\n\n\n\n<p>\u0637\u0647 , \u062e\u0627\u0644\u062f \u0639\u064a\u0633\u0649 <strong>. \u0645\u0644\u0627\u062d\u0642\u0629 \u0627\u0644\u0641\u0633\u0627\u062f \u0627\u0644\u0625\u062f\u0627\u0631\u064a<\/strong><\/p>\n\n\n\n<p><a href=\"http:\/\/www.azzaman.com\/azzaman\/articles\/2004\/03\/03-29\/802.htm\">http:\/\/www.azzaman.com\/azzaman\/articles\/2004\/03\/03-29\/802.htm<\/a><strong><\/strong><\/p>\n\n\n\n<p><strong>\u0627\u0644\u0641\u0633\u0627\u062f \u0627\u0644\u0625\u062f\u0627\u0631\u064a \u0648\u062c\u0631\u0627\u0626\u0645 \u0625\u0633\u0627\u0621\u0629 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u0627\u0644\u0633\u0644\u0637\u0629 \u0627\u0644\u0648\u0638\u064a\u0641\u064a\u0629<\/strong><\/p>\n\n\n\n<p><a href=\"http:\/\/news.naseej.com.sa\/detail.asp?InSectionID=1431&amp;InNewsItemID=123076\">http:\/\/news.naseej.com.sa\/detail.asp?InSectionID=1431&amp;InNewsItemID=123076<\/a><\/p>\n\n\n\n<p>\u0627\u0644\u0633\u064a\u0641 , \u062e\u0644\u064a\u0641\u0629 \u0639\u0628\u062f \u0627\u0644\u0644\u0647 . <strong>&nbsp;\u0645\u062a\u0649 \u0646\u0631\u0649 \u0622\u0644\u064a\u0629 \u0635\u062d\u064a\u062d\u0629 \u0644\u0645\u062d\u0627\u0631\u0628\u0629 \u0627\u0644\u0641\u0633\u0627\u062f<\/strong><\/p>\n\n\n\n<p><a href=\"http:\/\/www.alwatan.com.sa\/daily\/2002-10-19\/resders.htm\">http:\/\/www.alwatan.com.sa\/daily\/2002-10-19\/resders.htm<\/a><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re:&nbsp;&nbsp; Distributions 1&nbsp; <\/strong>&nbsp;(Code DIST1&nbsp; 102)<\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong>&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de r\u00e9unir quelques connaissances sur la th\u00e9orie des distributions.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res d\u2019analyse&nbsp; et d\u2019alg\u00e8bre&nbsp; de la licence de math\u00e9matiques fondamentales&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:&nbsp;<\/strong><\/p>\n\n\n\n<p>I- Espaces vectoriels topologiques<\/p>\n\n\n\n<p>I.1- Compl\u00e9ments sur la topologie<\/p>\n\n\n\n<p>I.2- Compl\u00e9ments sur les espaces vectoriels<\/p>\n\n\n\n<p>I.3- Propri\u00e9t\u00e9s g\u00e9n\u00e9rales des espaces vectoriels topologiques<\/p>\n\n\n\n<p>I.4- Espaces vectoriels topologiques localement convexe<\/p>\n\n\n\n<p>I.5-Limite inductive stricte d\u2019espaces vectoriels topologiques localement convexes<\/p>\n\n\n\n<p>I.6- Dualit\u00e9 et transposition<\/p>\n\n\n\n<p>II- Espaces fondamentaux<\/p>\n\n\n\n<p>II.5- Th\u00e9or\u00e8mes de densit\u00e9 (r\u00e9gularisation et troncature)<\/p>\n\n\n\n<p>II.6- Partition de l\u2019unit\u00e9<\/p>\n\n\n\n<p>II.7- Produit tensoriel de fonctions<\/p>\n\n\n\n<p>III- Distributions<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; III.1- Distributions<\/p>\n\n\n\n<p>III.2- Restriction, support et distributions \u00e0 support compact<\/p>\n\n\n\n<p>III.3- Produit multiplicatif d\u2019une distribution par une fonction<\/p>\n\n\n\n<p>III.4- D\u00e9rivation des distributions<\/p>\n\n\n\n<p>IV- Convolution des distributions<\/p>\n\n\n\n<p>IV.1- Fonctions d\u00e9finies par dualit\u00e9<\/p>\n\n\n\n<p>IV.2- Produit tensoriel de distributions<\/p>\n\n\n\n<p>IV.3- Produit convolutif de distributions<\/p>\n\n\n\n<p>IV.4- R\u00e9gularisation des distributions<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>40% travail continu et 60%&nbsp; Examen<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rence.<\/strong><\/p>\n\n\n\n<p>Khoan Vo-Khac., Distributions Analyse de Fourier Op\u00e9rateurs aux d\u00e9riv\u00e9es partielles,&nbsp;<\/p>\n\n\n\n<p>Tome I, Vuibert (1972).<\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re:&nbsp;&nbsp; Analyse Fonctionnelle 2<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement : <\/strong>Faisant suite au cours d&rsquo;Analyse fonctionnelle 1, le pr\u00e9sent cours traite essentiellement de la th\u00e9orie des op\u00e9rateurs lin\u00e9aires compacts auto-adjoints et leurs propri\u00e9t\u00e9s spectrales et pr\u00e9sente une introduction \u00e0 l&rsquo;analyse fonctionnelle non lin\u00e9aire avec quelques exemples d&rsquo;application aux \u00e9quations diff\u00e9rentielles, int\u00e9grales et abstraites. On y trouve \u00e0 la fois les aspects \u00ab abstraits \u00bb et \u00ab concrets \u00bb des concepts et r\u00e9sultats trait\u00e9s.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es : <\/strong>Introduction \u00e0 l\u2019analyse hilbertienne, Analyse fonctionnelle 1.<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re :<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1.&nbsp;&nbsp; Espaces de Hilbert<\/strong><\/p>\n\n\n\n<p>1.1 Propri\u00e9t\u00e9s \u00e9l\u00e9mentaires et exemples<\/p>\n\n\n\n<p>1.2 Projection orthogonale<\/p>\n\n\n\n<p>1.3 Familles orthonormales, bases hilbertiennes<\/p>\n\n\n\n<p>1.4 Th\u00e9or\u00e8me de Repr\u00e9sentation de Riesz, dual d&rsquo;un espace de Hilbert<\/p>\n\n\n\n<p><strong>Chapitre 2.&nbsp;&nbsp; Op\u00e9rateurs lin\u00e9aires sur des espaces de Hilbert<\/strong><\/p>\n\n\n\n<p>2.1 Adjoint d&rsquo;un op\u00e9rateur lin\u00e9aire born\u00e9<\/p>\n\n\n\n<p>2.2 Op\u00e9rateurs born\u00e9s auto-adjoints, normaux, unitaires et propri\u00e9t\u00e9s spectrales<\/p>\n\n\n\n<p>2.3 Op\u00e9rateur adjoint d&rsquo;un op\u00e9rateur lin\u00e9aire non born\u00e9<\/p>\n\n\n\n<p><strong>Chapitre 3.&nbsp;&nbsp; Op\u00e9rateurs lin\u00e9aires compacts<\/strong><\/p>\n\n\n\n<p>3.1 D\u00e9finition et exemples d&rsquo;op\u00e9rateurs lin\u00e9aires compacts<\/p>\n\n\n\n<p>3.2 Alternative de Fredholm<\/p>\n\n\n\n<p>3.3 Propri\u00e9t\u00e9s spectrales d&rsquo;un op\u00e9rateur compact<\/p>\n\n\n\n<p>3.4 Op\u00e9rateurs auto-adjoints compacts<\/p>\n\n\n\n<p>3.5 Application \u00e0 la r\u00e9solution d&rsquo;\u00e9quations int\u00e9grales lin\u00e9aires<\/p>\n\n\n\n<p><strong>Chapitre 4.&nbsp;&nbsp; Th\u00e9or\u00e8mes de points fixes des op\u00e9rateurs non lin\u00e9aires et applications<\/strong><\/p>\n\n\n\n<p>4.1 Principe de l&rsquo;application contractante<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.1.1 Points fixes d&rsquo;un op\u00e9rateur non lin\u00e9aire<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.1.2 Principe de l&rsquo;application contractante<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.1.3 Application \u00e0 la r\u00e9solution du probl\u00e8me de Cauchy pour une \u00e9quation diff\u00e9rentielle non lin\u00e9aire dans un espace de Banach<\/p>\n\n\n\n<p>4.2 Principe de Schauder<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.2.1 Th\u00e9or\u00e8me du point fixe de Brouwer<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.2.2 Op\u00e9rateurs compacts non lin\u00e9aires et leurs approximations<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.2.3 Principe du point fixe de Schauder<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.2.4 Application \u00e0 la r\u00e9solution de probl\u00e8mes aux limites et d&rsquo;\u00e9quations int\u00e9grales non lin\u00e9aires<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4.2.5 Quelques th\u00e9or\u00e8mes de points fixes d\u00e9coulant du principe de Schauder.<\/p>\n\n\n\n<p><strong>Chapitre 5.&nbsp;&nbsp; Les op\u00e9rateurs monotones et les in\u00e9quations variationnelles<\/strong><\/p>\n\n\n\n<p>5.1 Op\u00e9rateurs monotones, d\u00e9finitions et premi\u00e8res propri\u00e9t\u00e9s<br>5.2 Op\u00e9rateurs pseudo-monotones<br>5.4 In\u00e9quations variationnelles<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation: <\/strong><strong>Contr\u00f4le continu (40%), Examen (60%)<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences<\/strong>:<\/p>\n\n\n\n<p>1. V. Hutson, J.S. Pym and M.J. Cloud, Applications of Functional Analysis and Operator Theory, Elsevier Science, 2005.<\/p>\n\n\n\n<p>2. V. Tr\u00e9noguine, Analyse Fonctionnelle, Editions Mir, 1985.<\/p>\n\n\n\n<p>3. H. Brezis, Analyse Fonctionnelle Th\u00e9orie et Applications, Dunod, 2005<\/p>\n\n\n\n<p>4. A. Bressan, Lecture Notes on Functional Analysis With Applications to Linear Partial Differential Equations, American Mathematical Society, 2012<\/p>\n\n\n\n<p>5. B. Rynne, M.A. Youngson, Linear Functional Analysis, Springer, 2008<\/p>\n\n\n\n<p>6. E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley &amp; Sons, 1978.<\/p>\n\n\n\n<p>7. N. El Hage Hassan, Topologie g\u00e9n\u00e9rale et Espaces norm\u00e9s, Dunod, 2011.<\/p>\n\n\n\n<p>8. A. Kolmogorov, S. Fomine, El\u00e9ments de la th\u00e9orie des fonctions et de l&rsquo;analyse fonctionnelle, Editions Mir, 1973.<\/p>\n\n\n\n<p>9. D. Kinderlehrer, G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Society for Industrial and Applied Mathematics, 1987<\/p>\n\n\n\n<p>10. H. Le Dret, \u00c9quations aux d\u00e9riv\u00e9es partielles elliptiques non lin\u00e9aires, Springer, 2013<\/p>\n\n\n\n<p>11. R. E. Showalter, Monotone operators in Banach space and nonlinear PDFs, AMS, 1996<\/p>\n\n\n\n<p>12. E. Zeidler, Nonlinear functional analysis, Vol. 2,&nbsp; Part B., Springer, 1990.<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re:&nbsp;&nbsp; Statistique inf\u00e9rentielle<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong> (D\u00e9crire ce que l\u2019\u00e9tudiant est cens\u00e9 avoir acquis comme comp\u00e9tences apr\u00e8s le succ\u00e8s \u00e0 cette mati\u00e8re \u2013 maximum 3 lignes).&nbsp;&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de r\u00e9unir des connaissances sur la statistique math\u00e9matique (Estimation et tests d\u2019hypoth\u00e8ses)<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es (<\/strong>descriptif succinct des connaissances requises pour pouvoir suivre cet enseignement \u2013 Maximum 2 lignes).<\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res de probabilit\u00e9s et statistique de la licence math\u00e9matiques et master 1.&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1<\/strong>: Structures statistiques<\/p>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp; Structures domin\u00e9es<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Notion de statistiques<\/li>\n\n\n\n<li>Fonction de vraisemblance. Information de Fisher et de Kullback.<\/li>\n\n\n\n<li>In\u00e9galit\u00e9 de Cramer-Rao&nbsp;<\/li>\n\n\n\n<li>Exhaustivit\u00e9&nbsp; et libert\u00e9<\/li>\n<\/ul>\n\n\n\n<p><strong>Chapitre 2<\/strong>: L\u2019inf\u00e9rence statistique&nbsp;<\/p>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp; Notions de strat\u00e9gie et r\u00e8gles de d\u00e9cision<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Echantillonage&nbsp;: g\u00e9n\u00e9ralit\u00e9s sur l\u2019\u00e9chantillonage. Etude&nbsp; de quelques statistiques et comportement asymptotique des \u00e9chantillons. Les statistiques d\u2019ordre.<\/li>\n<\/ul>\n\n\n\n<p><strong>Chapitre 3&nbsp;<\/strong>: Estimation &nbsp;et tests&nbsp;&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Estimation ponctuelle et estimation ensembliste&nbsp;: d\u00e9finition et propri\u00e9t\u00e9s , estimateurs sans biais&nbsp;; consistance et efficacit\u00e9 des estimateurs.<\/li>\n\n\n\n<li>M\u00e9thodes d\u2019estimation et comportement asymptotique&nbsp;: m\u00e9thode de vraisemblance, m\u00e9thode des moments, intervalles de confiance.<\/li>\n<\/ul>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp; -G\u00e9n\u00e9ralit\u00e9s sur les tests d\u2019hypoth\u00e8ses<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp; &#8211; Lemme de Neyman-pearson<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>40% travail continu, 60% Examen.<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites internet, etc.).<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re:&nbsp;&nbsp; Optimisation avec contraintes<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : M\u00e9thodologie<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 5<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 2<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement <\/strong>:<\/p>\n\n\n\n<p>Ce cours traite&nbsp; de la r\u00e9solution des probl\u00e8mes d\u2019optimisation formul\u00e9s sous la forme des contraintes. Il vise \u00e0 donner \u00e0 l\u2019\u00e9tudiant les outils n\u00e9cessaires pour r\u00e9soudre un probl\u00e8me d\u2019optimisation sous un certain nombre de contraintes.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es :<\/strong><\/p>\n\n\n\n<p>Cours d\u2019analyse num\u00e9rique, topologie et optimisation sans contraintes<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1<\/strong><\/p>\n\n\n\n<p><strong>G\u00e9n\u00e9ralit\u00e9s<\/strong><\/p>\n\n\n\n<p>1.1 Rappels et notations de calcul diff\u00e9rentiel<\/p>\n\n\n\n<p>1.2 Notion de convexit\u00e9<\/p>\n\n\n\n<p>1.3 Conditions d\u2019optimalit\u00e9<\/p>\n\n\n\n<p>1.4 R\u00e9sultats d\u2019existence et d\u2019unicit\u00e9<\/p>\n\n\n\n<p><strong>Chapitre&nbsp; 2<\/strong><\/p>\n\n\n\n<p><strong>&nbsp;Minimisation avec contraintes<\/strong><\/p>\n\n\n\n<p>2.1 Introduction<\/p>\n\n\n\n<p>2.2 Cas des contraintes d\u2019\u00e9galit\u00e9s<\/p>\n\n\n\n<p>&nbsp;&nbsp; 2.2.1 Multiplicateurs de Lagrange<\/p>\n\n\n\n<p>2.3 Cas des contraintes d\u2019in\u00e9galit\u00e9s<\/p>\n\n\n\n<p>&nbsp;&nbsp; 2.3.1 Les Conditions de Karush-Kuhn-Tucker (KKT)<\/p>\n\n\n\n<p><strong>Chapitre&nbsp; 3<\/strong><\/p>\n\n\n\n<p><strong>Quelques m\u00e9thodes d\u2019optimisation<\/strong><\/p>\n\n\n\n<p>3.1 Introduction<\/p>\n\n\n\n<p>3.2 Les algorithmes sous contraintes<\/p>\n\n\n\n<p>&nbsp;&nbsp; 3.2.1 M\u00e9thode d\u2019Uzawa<\/p>\n\n\n\n<p>&nbsp;&nbsp; 3.2.2 M\u00e9thode du Gradient projet\u00e9<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;<\/strong>: <strong>40% travail continu, 60% Examen.<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences :<\/strong><\/p>\n\n\n\n<p>1.&nbsp; Robert M. Freund, Optimality Conditions for Constrained Optimization Problems, Massachusetts Institute of Technology (2004).<\/p>\n\n\n\n<p>2. G. Ciarlet, Introduction a l&rsquo;analyse num\u00e9rique matricielle et a l&rsquo;optimisation,<\/p>\n\n\n\n<p>Masson, Paris, (1985).<\/p>\n\n\n\n<p>3. J.C. Culioli, Introduction a l&rsquo;optimisation, Ellipses (1994).<\/p>\n\n\n\n<p>4. Laurent Guillop\u00e9, Optimisation sous contrainte, Universit\u00e9 de Nantes (2015)<\/p>\n\n\n\n<p>5. <a href=\"http:\/\/www.univ-oeb.dz\/images\/documentation\/Cours\/mi\/optimisation_hamaizia.pdf\">www.univ-oeb.dz\/images\/documentation\/Cours\/mi\/optimisation_hamaizia.pdf<\/a><\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re:&nbsp;&nbsp; Equations aux d\u00e9riv\u00e9s partielles<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : M\u00e9thodologie<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 2<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement : <\/strong>prise de contact avec les EDP et quelques-unes des m\u00e9thodes et des<\/p>\n\n\n\n<p>probl\u00e9matiques qui s\u2019y rattachent, apprendre quelques techniques de r\u00e9solution de chaque type.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es <\/strong>: Analyse, alg\u00e8bre, topologie<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re :<\/strong><\/p>\n\n\n\n<p><strong>Chapitre1 : Cas elliptique<\/strong><\/p>\n\n\n\n<p>1.1 S\u00e9parations des variables<\/p>\n\n\n\n<p>1.2 Etude du probl\u00e8me de Dirichlet pour le Laplacien (n=2,n=3)<\/p>\n\n\n\n<p>(Noyau de Poisson, Fonctions de Green pour la boule et le demi-plan)<\/p>\n\n\n\n<p><strong>Chapitre2 : Cas hyperbolique \u2013 Equations des ondes<\/strong><\/p>\n\n\n\n<p>2.1 Par s\u00e9paration des variables<\/p>\n\n\n\n<p>2.2 Repr\u00e9sentation de la solution<\/p>\n\n\n\n<p>2.3 Principe de Huygens (n=1, n=2)<\/p>\n\n\n\n<p>2.4 Cordes et plaques vibrantes (S\u00e9ries de Fourier)<\/p>\n\n\n\n<p><strong>Chapitre3 : Cas parabolique \u2013 Equation de la chaleur<\/strong><\/p>\n\n\n\n<p>3.1 Par s\u00e9paration des variables et superposition (S\u00e9ries de Fourier)<\/p>\n\n\n\n<p>3.2 Repr\u00e9sentation de la solution dans Rn, r\u00e9gularit\u00e9 de la solution.<\/p>\n\n\n\n<p>3.3 Equations particuli\u00e8res (Bernouilli-Ricati-Clairaut)<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation : Examen (60%), contr\u00f4le continu (40%)<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences<\/strong>:<\/p>\n\n\n\n<p>-J.Bass, Analyse math\u00e9matique Tome 2<\/p>\n\n\n\n<p>-Herv\u00e9 Reinhardt, Equations aux d\u00e9riv\u00e9es partielles-cours et exercices corrig\u00e9s<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S2&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; LATEX<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : D\u00e9couverte<\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 1<\/strong> <strong><\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong>&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de r\u00e9unir des connaissances sur quelques logiciels utiles en math\u00e9matiques.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les&nbsp; connaissances de bases en informatique.&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Latex&nbsp; et Latex beamer<\/li>\n\n\n\n<li>Scientifique Workplace<\/li>\n<\/ul>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>100%&nbsp; Examen<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites Internet, etc.).<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S2&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re: Thinking skills<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Transversale<\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 1<\/strong> <strong><\/strong><\/p>\n\n\n\n<p>\u0627\u0644\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a\u0629<strong> : <\/strong>\u064a\u0647\u062f\u0641 \u062a\u062f\u0631\u064a\u0633 \u0647\u0630\u0647 \u0627\u0644\u0645\u0627\u062f\u0629 \u0625\u0644\u0649 \u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0645\u062d\u0627\u0643\u0645\u0629 \u0627\u0644\u0639\u0642\u0644\u064a\u0629 \u0648\u0623\u0633\u0644\u0648\u0628 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0644\u062f\u0649 \u0627\u0644\u0637\u0627\u0644\u0628 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0628\u064a\u0627\u0646 \u0645\u0644\u0627\u0645\u062d \u0627\u0644\u0639\u0642\u0644\u064a\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629 \u0648\u0634\u0631\u0648\u0637 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0633\u0644\u064a\u0645 \u0648\u0627\u0644\u062a\u0646\u0628\u064a\u0647 \u0625\u0644\u0649 \u0628\u0639\u0636 \u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0627\u0639\u0648\u062c\u0627\u062c \u0641\u064a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0648\u0645\u0632\u0627\u0644\u0642\u0647.<\/p>\n\n\n\n<p><strong>\u0645\u062d\u062a\u0648\u064a \u0627\u0644\u0645\u0627\u062f\u0629:<\/strong><\/p>\n\n\n\n<p><strong>&#8211; \u0645\u062f\u062e\u0644 \u0645\u0641\u0627\u0647\u064a\u0645\u064a : <\/strong>\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0641\u0643\u064a\u0631\u060c \u062e\u0635\u0627\u0626\u0635\u0647\u060c \u0645\u0633\u062a\u0648\u064a\u0627\u062a\u0647 \u0648\u0623\u0646\u0648\u0627\u0639\u0647\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0628\u0646\u0627\u0621 \u0644\u0644\u0646\u0645\u0627\u0630\u062c\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0641\u0646 \u0637\u0631\u062d \u0627\u0644\u0623\u0633\u0626\u0644\u0629\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0645\u0646 \u0623\u062c\u0644 \u062a\u062e\u0637\u064a \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0642\u0627\u0626\u0645\u0629\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0648\u0627\u0644\u0644\u063a\u0629\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0648\u0627\u0644\u0639\u0648\u0627\u0637\u0641 &#8230;<\/p>\n\n\n\n<p><strong>&#8211; \u0645\u0639\u0627\u0644\u0645 \u0627\u0644\u0639\u0642\u0644\u064a\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629 \u0648\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0633\u0644\u064a\u0645<\/strong><\/p>\n\n\n\n<p><strong>&#8211; \u0645\u0646 \u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u0639\u0648\u062c :<\/strong> \u0625\u0635\u062f\u0627\u0631 \u0627\u0644\u0623\u062d\u0643\u0627\u0645 \u0627\u0644\u0645\u0633\u0628\u0642\u0629\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0633\u0644\u0628\u064a\u060c \u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u0633\u0627\u0631 \u0627\u0644\u0648\u0627\u062d\u062f\u060c \u0627\u0644\u062a\u0639\u0635\u0628 \u0648\u0627\u0644\u0648\u062b\u0648\u0642\u064a\u0629 \u0627\u0644\u0632\u0627\u0626\u062f\u0629\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0626\u064a\u060c \u0627\u0644\u062a\u0647\u0648\u064a\u0644 \u0648\u0627\u0644\u0645\u0628\u0627\u0644\u063a\u0629\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u062a\u0628\u0631\u064a\u0631\u064a\u060c \u0627\u0644\u062a\u0639\u0645\u064a\u0645\u060c \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u0628\u0633\u0651\u0637 (\u0627\u0644\u0633\u0651\u0637\u062d\u064a)\u060c \u062a\u0623\u062b\u064a\u0631 \u0627\u0644\u0627\u0646\u0637\u0628\u0627\u0639\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u0649 \u0648\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0639\u062c\u0648\u0644 &#8230;<\/p>\n\n\n\n<p><strong>&#8211; \u0627\u0644\u0645\u0631\u0648\u0646\u0629 \u0627\u0644\u0630\u0647\u0646\u064a\u0629 \u0648\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u062a\u0635\u0644\u0628<\/strong><\/p>\n\n\n\n<p><strong>&#8211; \u0645\u0648\u0627\u0631\u062f \u062a\u0646\u0645\u064a\u0629 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 :<\/strong> \u0623\u062d\u062f\u0627\u062b \u0627\u0644\u062d\u064a\u0627\u0629\u060c \u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0629\u060c \u0627\u0644\u0642\u0631\u0627\u0621\u0629 \u0648\u0627\u0644\u0627\u0637\u0644\u0627\u0639\u060c \u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u062a\u0630\u0629\u060c \u0627\u0644\u062d\u0648\u0627\u0631\u060c \u0627\u0644\u062a\u0623\u0645\u0644 &#8230;<\/p>\n\n\n\n<p><strong>&#8211; \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0646\u0627\u0642\u062f : <\/strong>\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0646\u0627\u0642\u062f\u060c \u0645\u0639\u0627\u064a\u064a\u0631 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0646\u0627\u0642\u062f\u060c \u0645\u0647\u0627\u0631\u0627\u062a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0646\u0627\u0642\u062f<\/p>\n\n\n\n<p><strong>&#8211; \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0627\u0628\u062f\u0627\u0639\u064a \u0648\u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a<\/strong><\/p>\n\n\n\n<p><strong>\u0645\u0631\u0627\u062c\u0639 :<\/strong><\/p>\n\n\n\n<p>&#8211; <strong>\u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u062a\u0641\u0643\u064a\u0640\u0640\u0640\u0631 (\u0645\u0641\u0627\u0647\u064a\u0645 \u0648\u062a\u0637\u0628\u064a\u0642\u0627\u062a)<\/strong>\u060c \u0623.\u062f . \u0641\u062a\u062d\u064a \u0639\u0628\u062f \u0627\u0644\u0631\u062d\u0645\u0646 \u062c\u0631\u0648\u0627\u0646\u060c \u0627\u0644\u0623\u0631\u062f\u0646\u060c \u062f\u0627\u0631 \u0627\u0644\u0641\u0643\u0631\u060c 2007.<\/p>\n\n\n\n<p>&#8211; <strong>\u0627\u0644\u0637\u0631\u064a\u0642 \u0625\u0644\u0649 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u0646\u0637\u0642\u064a<\/strong>\u060c \u062a\u0623\u0644\u064a\u0641 \u0648\u0644\u064a\u0645 \u0634\u0627\u0646\u0631\u060c \u062a\u0631\u062c\u0645\u0629 \u062f. \u0639\u0637\u064a\u0629 \u0645\u062d\u0645\u0648\u062f \u0647\u0646\u0627\u060c \u0645\u0635\u0631\u060c \u0645\u0643\u062a\u0628\u0629 \u0627\u0644\u0646\u0647\u0636\u0629 \u0627\u0644\u0645\u0635\u0631\u064a\u0629.<\/p>\n\n\n\n<p>&#8211; <strong>\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0648\u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0623\u0639\u0648\u062c<\/strong>\u060c \u062a\u0623\u0644\u064a\u0641 \u062f. \u0631\u0648\u0628\u0631\u062a \u062b\u0627\u0648\u0644\u0633\u060c \u062a\u0631\u062c\u0645\u0629 \u062d\u0633\u0646 \u0627\u0644\u0643\u0631\u0645\u064a\u060c \u0627\u0644\u0643\u0648\u064a\u062a-\u0633\u0644\u0633\u0644\u0629 \u0639\u0627\u0644\u0645 \u0627\u0644\u0645\u0639\u0631\u0641\u0629<\/p>\n\n\n\n<p>&#8211; <strong>\u062e\u0637\u0648\u0629 \u0646\u062d\u0648 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0642\u0648\u064a\u0645<\/strong>\u060c \u0623.\u062f . \u0639\u0628\u062f \u0627\u0644\u0643\u0631\u064a\u0645 \u0628\u0643\u0627\u0631\u060c \u0627\u0644\u0623\u0631\u062f\u0646\u060c \u062f\u0627\u0631 \u0627\u0644\u0625\u0639\u0644\u0627\u0645\u060c 2009<\/p>\n\n\n\n<p>&#8211; <strong>\u0641\u0635\u0648\u0644 \u0641\u064a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u0648\u0636\u0648\u0639\u064a<\/strong>\u060c \u0623.\u062f . \u0639\u0628\u062f \u0627\u0644\u0643\u0631\u064a\u0645 \u0628\u0643\u0627\u0631.<\/p>\n\n\n\n<p>&#8211; <strong>\u0627\u0644\u0627\u0646\u0633\u0627\u0646 \u0627\u0644\u0641\u0639\u0627\u0644 : \u0627\u0644\u0645\u0632\u0627\u064a\u0627 \u0627\u0644\u0639\u0634\u0631 \u0644\u0644\u0625\u0646\u0633\u0627\u0646 \u0627\u0644\u0645\u062a\u0641\u0648\u0651\u0642<\/strong>\u060c \u062c\u0645\u0627\u0644 \u062c\u0645\u0627\u0644 \u0627\u0644\u062f\u064a\u0646\u060c \u0633\u0648\u0631\u064a\u0627\u060c \u062f\u0627\u0631 \u0627\u0644\u0641\u0643\u0631\u060c 2009.<\/p>\n\n\n\n<p>&#8211; <strong>\u062a\u0643\u0648\u064a\u0646 \u0627\u0644\u0645\u0641\u0643\u0631<\/strong>\u060c \u0623.\u062f . \u0639\u0628\u062f \u0627\u0644\u0643\u0631\u064a\u0645 \u0628\u0643\u0627\u0631\u060c \u0627\u0644\u0645\u0645\u0644\u0643\u0629 \u0627\u0644\u0639\u0631\u0628\u064a\u0629 \u0627\u0644\u0633\u0639\u0648\u062f\u064a\u0629\u060c \u062f\u0627\u0631 \u0648\u062c\u0648\u0647 \u0644\u0644\u0646\u0634\u0631 \u0648\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u060c 2010.<\/p>\n\n\n\n<p>&#8211; <strong>\u0639\u0635\u0631\u0646\u0627 \u0648\u0627\u0644\u0639\u064a\u0634 \u0641\u064a \u0632\u0645\u0627\u0646\u0647 \u0627\u0644\u0635\u0639\u0628<\/strong> \u060c \u0623.\u062f . \u0639\u0628\u062f \u0627\u0644\u0643\u0631\u064a\u0645 \u0628\u0643\u0627\u0631\u060c \u0633\u0648\u0631\u064a\u0627\u060c \u062f\u0627\u0631 \u0627\u0644\u0642\u0644\u0645\u060c 2007.<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; Distributions 2 <\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong>&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de compl\u00e9ter leurs&nbsp;&nbsp; connaissances sur les distributions.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res&nbsp; d\u2019analyse&nbsp; de la licence math\u00e9matiques et master 1.&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<p>I- Espaces de Sobolev<\/p>\n\n\n\n<p>I.4- Quelques r\u00e9sultats dans le cas&nbsp; d\u2019un intervalle ouvert de<\/p>\n\n\n\n<p>II- Distributions temp\u00e9r\u00e9es<\/p>\n\n\n\n<p>II.1- Espace de Schwartz<\/p>\n\n\n\n<p>II.2- Distributions temp\u00e9r\u00e9es<\/p>\n\n\n\n<p>II.3- Op\u00e9rateurs de multiplication<\/p>\n\n\n\n<p>II.4- Op\u00e9rateurs de convolution<\/p>\n\n\n\n<p>III- Transformation de Fourier<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; III.4- Transformation de Fourier des distributions temp\u00e9r\u00e9es<\/p>\n\n\n\n<p>IV- Espaces de Sobolev&nbsp;<\/p>\n\n\n\n<p>IV.1- Espaces<\/p>\n\n\n\n<p>IV.2- Th\u00e9or\u00e8me d\u2019injection de Sobolev&nbsp;<\/p>\n\n\n\n<p>IV.3- Injection compacte<\/p>\n\n\n\n<p>IV.4- Traces<\/p>\n\n\n\n<p>IV.5- Propri\u00e9t\u00e9s d\u2019un demi-espace<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>40% travail continu, 60% Examen.<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences:<\/strong><\/p>\n\n\n\n<p>&#8211; KHOAN V-K., Distributions Analyse de Fourier Op\u00e9rateurs aux d\u00e9riv\u00e9es partielles,<\/p>\n\n\n\n<p>&nbsp; Tome II, Vuibert (1972).<\/p>\n\n\n\n<p>&nbsp;&#8211; BREZIS H., Analyse fonctionnelle th\u00e9orie et applications, Masson (1983).<\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; Th\u00e9orie variationnelle&nbsp; des \u00e9quations elliptiques<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong><\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; d\u2019acqu\u00e9rir&nbsp; des&nbsp; connaissances sur les probl\u00e8mes elliptiques.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res d\u2019analyse&nbsp; de la licence math\u00e9matiques et master 1.&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<p>I- Probl\u00e8mes variationnels elliptiques abstraits<\/p>\n\n\n\n<p>I.1- Quelques rappels sur les espaces de Hilbert<\/p>\n\n\n\n<p>I.2- Th\u00e9or\u00e8me de Lax-Milgram<\/p>\n\n\n\n<p>II- Probl\u00e8mes elliptiques lin\u00e9aires du second ordre<\/p>\n\n\n\n<p>II.1- Quelques rappels sur les espaces de Sobolev&nbsp;et sur l\u2019analyse vectoriel<\/p>\n\n\n\n<p>II.2- Probl\u00e8mes aux limites elliptiques du second ordre<\/p>\n\n\n\n<p>II.3- Formulation variationnelle et notion de solution faible<\/p>\n\n\n\n<p>II.4- \u00c9tude de quelques cas&nbsp;: probl\u00e8mes de Dirichlet, probl\u00e8mes de Neumann,<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; probl\u00e8mes m\u00eal\u00e9s<\/p>\n\n\n\n<p>III- R\u00e9gularit\u00e9 des solutions faibles<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; III.1- R\u00e9gularit\u00e9 \u00e0 l\u2019int\u00e9rieur<\/p>\n\n\n\n<p>III.2- R\u00e9gularit\u00e9 sur la fronti\u00e8re<\/p>\n\n\n\n<p>IV- Principe du maximum<\/p>\n\n\n\n<p>V- Introduction \u00e0 la th\u00e9orie spectrale des probl\u00e8mes aux limites elliptiques<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;&nbsp; 40% travail continu, 60% examen&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences <\/strong>:<\/p>\n\n\n\n<p>&#8211; H. BREZIS, Analyse fonctionnelle th\u00e9orie et applications, Masson, Paris (1983).<\/p>\n\n\n\n<p>&#8211; L.C.&nbsp; EVANS: Partial Di\ufb00erential Equations, Graduate Studies in Mathematics, vol. 19,<\/p>\n\n\n\n<p>American Mathematical Society, Providence, Rhode Island (1998)<\/p>\n\n\n\n<p>&nbsp;&#8211; P.-A. RAVIART &amp;&nbsp; J. M. THOMAS, Introduction \u00e0 l\u2019analyse num\u00e9rique des \u00e9quations<\/p>\n\n\n\n<p>aux d\u00e9riv\u00e9es partielles. Masson, Paris (1983).<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; Processus al\u00e9atoires et fiabilit\u00e9 des syst\u00e8mes<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 6<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 3<\/strong> <strong><\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong> <strong><\/strong><\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de r\u00e9unir des connaissances sur la th\u00e9orie des processus al\u00e9atoires et leurs applications et&nbsp; la fiabilit\u00e9 des syst\u00e8mes.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res&nbsp; de probabilit\u00e9s de la licence math\u00e9matiques et master 1.&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<p><strong>Chapitre 1<\/strong>&nbsp;: Processus Al\u00e9atoires<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li>G\u00e9n\u00e9ralit\u00e9s sur les processus Al\u00e9atoires\n<ol class=\"wp-block-list\">\n<li>Processus de naissance et de mort<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<p>1.3 Chaines de Markov \u00e0 temps discret<\/p>\n\n\n\n<p>1.3.1&nbsp; D\u00e9finition et propri\u00e9t\u00e9s.<\/p>\n\n\n\n<p>1.3.2&nbsp; Chaine trace, classification des \u00e9tats.<\/p>\n\n\n\n<p>1.3.3 Probabilit\u00e9s invariantes,&nbsp; r\u00e9versibilit\u00e9<\/p>\n\n\n\n<p>1.3.4 Chaines irr\u00e9ductibles, chaines ap\u00e9riodiques.<\/p>\n\n\n\n<p>1.3.5 Th\u00e9or\u00e8me ergodique.<\/p>\n\n\n\n<p><strong>Chapitre 2&nbsp;:<\/strong>&nbsp;Introduction \u00e0 la fiabilit\u00e9<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mesures&nbsp; de performances\n<ul class=\"wp-block-list\">\n<li>Taux de hasard, de d\u00e9faillance, de r\u00e9paration<ul><li>Les formules de base<\/li><\/ul><ul><li>Taux de d\u00e9faillance monotone<\/li><\/ul><ul><li>Loi NBU<\/li><\/ul><ul><li>Deux familles de lois classiques en fiabilit\u00e9<\/li><\/ul>\n<ul class=\"wp-block-list\">\n<li>G\u00e9n\u00e9ralisation de la notion de taux de hasard.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Chapitre3<\/strong>:&nbsp; Fiabilit\u00e9 des syst\u00e8mes Coh\u00e9rents<\/p>\n\n\n\n<p>3.1&nbsp; Propri\u00e9t\u00e9s des syst\u00e8mes coh\u00e9rents<\/p>\n\n\n\n<p>3.2 Formule et encadrement de la fiabilit\u00e9 des syst\u00e8mes<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>40% travail continu, 60% Examen.<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites Internet, etc.).<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li><strong>&nbsp;<\/strong>Bon, J.-L., 1995. Fiabilit\u00e9 des syst\u00e8mes. M\u00e9thodes math\u00e9matiques. Masson, Paris.<\/li>\n\n\n\n<li>Cocozza-Thivent C., Processus stochastiques et fiabilit\u00e9 des syst\u00e8mes, Springer, 1997.<\/li>\n<\/ol>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; Th\u00e9orie&nbsp; du&nbsp; contr\u00f4le<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : M\u00e9thodologie<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 2<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong>&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de r\u00e9unir quelques connaissances sur la th\u00e9orie de contr\u00f4le (contr\u00f4labilit\u00e9 et observabilit\u00e9)<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res d\u2019analyse&nbsp;&nbsp; de la licence de math\u00e9matiques fondamentales&nbsp;<\/p>\n\n\n\n<p>&nbsp;<strong>Contenu de la mati\u00e8re&nbsp;:&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>&nbsp;<\/strong><strong>Chapitre 1<\/strong>: Contr\u00f4labilit\u00e9 et observabilit\u00e9 en dimension finie<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Contr\u00f4labilit\u00e9<\/strong><\/li>\n<\/ul>\n\n\n\n<p>D\u00e9finitions,&nbsp; Op\u00e9rateur de contr\u00f4labilit\u00e9,<\/p>\n\n\n\n<p>Gramien de contr\u00f4labilit\u00e9. Caract\u00e9risations de la contr\u00f4labilit\u00e9.<\/p>\n\n\n\n<p>Contr\u00f4le optimal. Caract\u00e9risation.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Observabilit\u00e9<\/strong><\/li>\n<\/ul>\n\n\n\n<p>D\u00e9finitions, Op\u00e9rateur de l\u2019observabilit\u00e9,<\/p>\n\n\n\n<p>Gramien de l\u2019observabilit\u00e9, In\u00e9galit\u00e9 de .l\u2019observabilit\u00e9.<\/p>\n\n\n\n<p>Contr\u00f4labilit\u00e9 et in\u00e9galit\u00e9 de l\u2019observabilit\u00e9<\/p>\n\n\n\n<p>Crit\u00e8re de Kalman.<\/p>\n\n\n\n<p><strong>Chapitre 2:<\/strong> Stabilisation en dimension finie<\/p>\n\n\n\n<p>D\u00e9finitions : stabilisation forte, stabilisation exponentielle, stabilisation faible.<\/p>\n\n\n\n<p>Equivalence entre les trois notions en dimension finie.<\/p>\n\n\n\n<p>Crit\u00e8re de stabilisation en dimension finie.<\/p>\n\n\n\n<p><strong>Chapitre 3:<\/strong> Introduction \u00e0&nbsp; la th\u00e9orie des semi groupes.<\/p>\n\n\n\n<p>Motivations.<\/p>\n\n\n\n<p>D\u00e9finitions et propri\u00e9t\u00e9s.<\/p>\n\n\n\n<p>G\u00e9n\u00e9rateur infinit\u00e9simal, propri\u00e9t\u00e9s.<\/p>\n\n\n\n<p><strong>Mode d.\u00e9valuation: 40% travail continu, 60% Examen.<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences:<\/strong> (Livres, Polycopi\u00e9s, Sites internet, etc &#8230;).<\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S3&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 de la mati\u00e8re&nbsp;: <a href=\"https:\/\/www.google.dz\/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=8&amp;cad=rja&amp;uact=8&amp;ved=0ahUKEwjwv6rejLTKAhWHW5AKHZzEDeEQFghVMAc&amp;url=http%3A%2F%2Fwww.lps.ens.fr%2F%7Evincent%2Fch1e.pdf&amp;usg=AFQjCNFjWsvQAHrt4J1E6pJCAUhUKKeocg&amp;bvm=bv.112064104,d.bGQ\">Syst\u00e8mes dynamiques et introduction au chaos<\/a><\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : M\u00e9thodologie<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 5<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 2<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement&nbsp;:<\/strong><\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; d\u2019acqu\u00e9rir&nbsp; des&nbsp; connaissances sur les syst\u00e8mes dynamiques et Chaos.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Equations d\u2019ordre sup\u00e9rieur, Syst\u00e8mes lin\u00e9aires.<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re :<\/strong><\/p>\n\n\n\n<p><strong>Chapitre1 :<\/strong> <strong>Syst\u00e8mes dynamiques lin\u00e9aires<\/strong><\/p>\n\n\n\n<p>2-1 Les syst\u00e8mes dynamiques<\/p>\n\n\n\n<p>2-2 Espaces des phases<\/p>\n\n\n\n<p>2-3 Points fixes, sous espaces invariants<\/p>\n\n\n\n<p><strong>Chapitre2 : Syst\u00e8mes dynamiques non lin\u00e9aires<\/strong><\/p>\n\n\n\n<p>1-1 Les syst\u00e8mes autonomes et non autonomes<\/p>\n\n\n\n<p>1-2 Les syst\u00e8mes conservatifs et non conservatifs<\/p>\n\n\n\n<p>1-3 Exposants de Lyapunov<\/p>\n\n\n\n<p><strong>Chapitre3 : Existence et caract\u00e9risation du chaos&nbsp;<\/strong><\/p>\n\n\n\n<p>3-1 Le chaos d\u00e9terministe<\/p>\n\n\n\n<p>3-2 Caract\u00e9risations du chaos, sensibilit\u00e9s aux conditions initiales<\/p>\n\n\n\n<p>3-3 Caract\u00e9risations du chaos, le signe des exposants de Lyapunov<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation : <\/strong><strong>contr\u00f4le continu (40%), Examen (60%)<\/strong><\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rence :<\/strong><\/p>\n\n\n\n<p>1- M. Roseau : Equations diff\u00e9rentielles.<\/p>\n\n\n\n<p>2- V.S. Anishchenko, \u201cNonlinear dynamics of chaotic and stochastic systems\u00a0\u00bb Springer, 2002.<\/p>\n\n\n\n<p>3- V. S. Anishchenko,\u00a0\u00bb Dynamical chaos- Models and experiments\u00a0\u00bb, World scientific,<\/p>\n\n\n\n<p>1995.<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S3 &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; S\u00e9minaires<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : D\u00e9couverte<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 1<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong><\/p>\n\n\n\n<p>Cette mati\u00e8re permettra aux \u00e9tudiants&nbsp; de savoir comment pr\u00e9parer et r\u00e9diger &nbsp;des m\u00e9moires \u00e9crits et des expos\u00e9s oraux en math\u00e9matiques. Les th\u00e8mes seront donn\u00e9s&nbsp; par l\u2019enseignant de la mati\u00e8re &nbsp;au d\u00e9but du semestre 3.<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res&nbsp; de math\u00e9matiques du&nbsp; master 1 et de la licence de math\u00e9matiques.&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<p>Les th\u00e8mes seront sur&nbsp;:&nbsp;<\/p>\n\n\n\n<p>-Probabilit\u00e9s, statistique et Fiabilit\u00e9<\/p>\n\n\n\n<p>-Analyse fonctionnelle.<\/p>\n\n\n\n<p>-Optimisation<\/p>\n\n\n\n<p>-Analyse num\u00e9rique<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>100% travail continu.<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites internet, etc.).<\/p>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;:&nbsp;&nbsp; S3&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; R\u00e9daction scientifique<\/strong><\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Transversale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 1<\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement&nbsp;: <\/strong>Ce cours apprend \u00e0 l\u2019\u00e9tudiant la m\u00e9thodologie pour \u00e9laborer un travail scientifique. Il l\u2019assiste dans les op\u00e9rations de r\u00e9daction et de pr\u00e9sentation de ses contributions.<\/p>\n\n\n\n<p><strong>Connaissances requises&nbsp;: <\/strong>rien<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li>D\u00e9marche scientifique pour aborder les probl\u00e9matiques<\/li>\n\n\n\n<li>Recherche et collecte de la documentation<\/li>\n\n\n\n<li>D\u00e9marche de r\u00e9daction: compte-rendu, rapport, m\u00e9moire de fin d\u2019\u00e9tude, article de recherche<\/li>\n\n\n\n<li>Template<\/li>\n\n\n\n<li>D\u00e9marche de pr\u00e9sentation d\u2019un travail d\u2019\u00e9tude ou de recherche<\/li>\n\n\n\n<li>Les r\u00e8glements universitaires<\/li>\n\n\n\n<li>La fraude et le plagiat&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/li>\n<\/ol>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>100% examen.<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences&nbsp;:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>L. Blaxter, C. Hughes &amp; M. Tight, How to Research Buckingham: Open University Press, 1998.<\/li>\n\n\n\n<li>J. Collis, R. Hussey, Business Research: a practical guide for undergraduate and postgraduate students,Second edition, Basingstoke: Palgrave Macmillan, 2003.<\/li>\n\n\n\n<li>M, Denscombe, Ground Rules for Good Research, Maidenhead: Open University Press, 2002.<\/li>\n<\/ul>\n\n\n\n<p><strong>Intitul\u00e9 du Master&nbsp;:&nbsp;&nbsp;&nbsp; Math\u00e9matiques appliqu\u00e9es<\/strong><\/p>\n\n\n\n<p><strong>Semestre&nbsp;: S4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Intitul\u00e9 du la mati\u00e8re:&nbsp;&nbsp; M\u00e9moire<\/strong>&nbsp;<\/p>\n\n\n\n<p><strong>Unit\u00e9 d\u2019enseignement : Fondamentale<\/strong><\/p>\n\n\n\n<p><strong>Cr\u00e9dits :&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 30<\/strong><\/p>\n\n\n\n<p><strong>Coefficient : 30<\/strong><strong><\/strong><\/p>\n\n\n\n<p><strong>Objectifs de l\u2019enseignement<\/strong>&nbsp;<\/p>\n\n\n\n<p>Cette mati\u00e8re est consacr\u00e9 \u00e0 pr\u00e9parer un m\u00e9moire sur un th\u00e8me donn\u00e9 par l&rsquo;enseignant encadreur au d\u00e9but du semestre 4&nbsp;<\/p>\n\n\n\n<p><strong>Connaissances pr\u00e9alables recommand\u00e9es<\/strong><\/p>\n\n\n\n<p>Avoir acquis les mati\u00e8res&nbsp; de math\u00e9matiques du&nbsp; master 1 et le S3 du master et de la licence de math\u00e9matiques.&nbsp;<\/p>\n\n\n\n<p><strong>Contenu de la mati\u00e8re&nbsp;:<\/strong><\/p>\n\n\n\n<p>&#8211; Th\u00e8mes de probabilit\u00e9s et statistique<\/p>\n\n\n\n<p>&#8211; Th\u00e8mes d&rsquo;analyse<\/p>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation&nbsp;:&nbsp;<\/strong>100% travail continu (soutenance).<\/p>\n\n\n\n<p><strong>R\u00e9f\u00e9rences &nbsp; <\/strong>&nbsp;(Livres et polycopi\u00e9s,&nbsp; sites internet, etc.).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>D\u00e9partement de Math\u00e9matiques et d&rsquo;Informatique Nom du programme : Master en Math\u00e9matiques appliqu\u00e9es&nbsp; Niveau : Master Domaine&nbsp;: Math\u00e9matiques et informatique Fili\u00e8re&nbsp;: Math\u00e9matiques Sp\u00e9cialit\u00e9&nbsp;: Math\u00e9matiques appliqu\u00e9es&nbsp; Ann\u00e9e universitaire&nbsp;: 2022\/2023 Description du programme : Domaine&nbsp;: Math\u00e9matiques et informatique Fili\u00e8re&nbsp;: Math\u00e9matiques Sp\u00e9cialit\u00e9&nbsp;: Math\u00e9matiques appliqu\u00e9es&nbsp; Ann\u00e9e universitaire&nbsp;: 2022\/2023 Contexte et objectifs de la formation Conditions d\u2019acc\u00e8s&nbsp;: Licence en Math\u00e9matiques &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6847","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.univ-oeb.dz\/fsesnv\/wp-json\/wp\/v2\/pages\/6847","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.univ-oeb.dz\/fsesnv\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.univ-oeb.dz\/fsesnv\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.univ-oeb.dz\/fsesnv\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.univ-oeb.dz\/fsesnv\/wp-json\/wp\/v2\/comments?post=6847"}],"version-history":[{"count":0,"href":"https:\/\/www.univ-oeb.dz\/fsesnv\/wp-json\/wp\/v2\/pages\/6847\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.univ-oeb.dz\/fsesnv\/wp-json\/wp\/v2\/media?parent=6847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}