{"id":411,"date":"2025-09-26T10:03:28","date_gmt":"2025-09-26T09:03:28","guid":{"rendered":"https:\/\/unv-ebolowa.cm\/?p=411"},"modified":"2025-09-26T10:03:31","modified_gmt":"2025-09-26T09:03:31","slug":"introduction-a-lanalyse-et-a-lalgebre-sba111","status":"publish","type":"post","link":"https:\/\/unv-ebolowa.cm\/index.php\/en\/2025\/09\/26\/introduction-a-lanalyse-et-a-lalgebre-sba111\/","title":{"rendered":"INTRODUCTION A L\u2019ANALYSE ET A L\u2019ALGEBRE &#8211; SBA111"},"content":{"rendered":"\n<p><strong>Fili\u00e8re et option : <\/strong>Sciences Fondamentales de Base et Appliqu\u00e9es (Tronc commun Scientifiques)&nbsp;; Niveau I<\/p>\n\n\n\n<p><strong>Enseignant :<\/strong> Dr NOTUE KADJIE Arnaud<\/p>\n\n\n\n<p><strong>Disponibilit\u00e9 :<\/strong>&nbsp;&nbsp; permanent &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>Contact :<\/strong> Tel : <strong>6 91 76 69 78<\/strong><\/p>\n\n\n\n<p><strong>P\u00e9riode du cours :<\/strong> Semestre 1 (octobre- f\u00e9vrier)<\/p>\n\n\n\n<p><strong>R\u00e9partition du volume horaire (CM<\/strong> : 30 heures. <strong>TD<\/strong> : 10 heures&nbsp;; <strong>TPE<\/strong> : 5 heures<strong>) Cr\u00e9dit<\/strong> : 3<br><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Description du cours<\/strong><\/p>\n\n\n\n<p><strong>Objectifs g\u00e9n\u00e9raux<\/strong><\/p>\n\n\n\n<p>L\u2019objectif principal de ce cours est de fournir aux \u00e9tudiants les outils et la rigueur n\u00e9cessaires pour comprendre et manipuler les concepts fondamentaux de l\u2019analyse math\u00e9matique, en vue d\u2019applications ult\u00e9rieures en ing\u00e9nierie et autres disciplines scientifiques.<\/p>\n\n\n\n<p><strong>Contenu du cours<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Notions pr\u00e9liminaires (Ensembles num\u00e9riques, Intervalles, valeur absolue et in\u00e9galit\u00e9s, Principe de borne sup\u00e9rieure et borne inf\u00e9rieure)<\/li>\n\n\n\n<li>Suites num\u00e9riques<\/li>\n\n\n\n<li>Fonctions r\u00e9elles d\u2019une variable r\u00e9elle<\/li>\n\n\n\n<li>D\u00e9rivation des fonctions<\/li>\n<\/ul>\n\n\n\n<p><strong>Apprentissage vis\u00e9<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Application de l\u2019analyse<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-mecanique-classique\">M\u00e9canique classique :<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Utilisation des d\u00e9riv\u00e9es pour calculer la vitesse et l\u2019acc\u00e9l\u00e9ration d\u2019un objet en mouvement.\n<ul class=\"wp-block-list\">\n<li>\u00c9quations diff\u00e9rentielles pour mod\u00e9liser la dynamique des syst\u00e8mes (lois de Newton, oscillateurs harmoniques).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-electricite-et-magnetisme\">\u00c9lectricit\u00e9 et magn\u00e9tisme :<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>L\u2019int\u00e9gration permet de calculer le travail d\u2019une force \u00e9lectrique.\n<ul class=\"wp-block-list\">\n<li>L\u2019analyse des s\u00e9ries et des transform\u00e9es (Fourier, Laplace) aide \u00e0 r\u00e9soudre les circuits \u00e9lectriques.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-thermodynamique\">Thermodynamique :<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>L\u2019\u00e9tude des fonctions et des d\u00e9riv\u00e9es permet d\u2019optimiser les \u00e9changes thermiques.\n<ul class=\"wp-block-list\">\n<li>Int\u00e9gration pour calculer l\u2019\u00e9nergie interne et l\u2019entropie.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-traitement-du-signal-et-des-images\">Traitement du signal et des images :<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Transform\u00e9e de Fourier pour analyser les signaux audios et images.\n<ul class=\"wp-block-list\">\n<li>Filtrage num\u00e9rique et compression d\u2019images (JPEG, MP3).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp; <strong>Pr\u00e9requis<\/strong><\/p>\n\n\n\n<p>Alg\u00e8bre \u2013 notions de fonctions \u2013 Bases logique en math\u00e9matiques \u2013 Suites num\u00e9riques<\/p>\n\n\n\n<p><strong>Programme et calendrier<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Semaine<\/strong><strong><\/strong><\/td><td><strong>Contenus<\/strong><strong><\/strong><\/td><td><strong>Activit\u00e9s<\/strong><strong><\/strong><\/td><td><strong>Travail pr\u00e9alable<\/strong><\/td><\/tr><tr><td>Semaine 1<\/td><td>Acqu\u00e9rir les bases du raisonnement math\u00e9matique<\/td><td>Comprendre et utiliser les notions de logique math\u00e9matiqueD\u00e9monstration math\u00e9matique<\/td><td>R\u00e9viser les notions de la classe de Terminale Scientifique<\/td><\/tr><tr><td>Semaine 2<\/td><td>Ma\u00eetriser les notions fondamentales des ensembles et des fonctions<\/td><td>Conna\u00eetre les ensembles num\u00e9riquesComprendre la notion de fonction, les propri\u00e9t\u00e9s fondamentales<\/td><td>R\u00e9viser les notions de la classe de Terminale Scientifique<\/td><\/tr><tr><td>Semaine 3<\/td><td>\u00c9tudier la notion de suite et de limite<\/td><td>D\u00e9finir et analyser la convergence des suites num\u00e9riques.Calculer des limites de suites et utiliser des crit\u00e8res de convergence<\/td><td>R\u00e9viser les notions de la classe de Terminale Scientifique<\/td><\/tr><tr><td>Semaine 4<\/td><td>Notion de continuit\u00e9 d\u2019une fonction<\/td><td>D\u00e9finition et propri\u00e9t\u00e9s des fonctions continues.Th\u00e9or\u00e8mes fondamentaux<\/td><td>R\u00e9viser les notions de la classe de Terminale Scientifique<\/td><\/tr><tr><td>Semaine 5<\/td><td>Notion de d\u00e9rivation d\u2019une fonction<\/td><td>D\u00e9finition et interpr\u00e9tation g\u00e9om\u00e9trique de la d\u00e9riv\u00e9e.R\u00e8gles de d\u00e9rivation et \u00e9tude des fonctions d\u00e9rivablesApplications : approximation lin\u00e9aire, \u00e9tude des variations, optimisation.<\/td><td>R\u00e9viser les notions de la classe de Terminale Scientifique<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Mode d\u2019\u00e9valuation<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>P\u00e9riode<\/td><td>Type d\u2019examen \/ Comp\u00e9tences vis\u00e9es<\/td><td>Pourcentage<\/td><\/tr><tr><td>Semaine 3<\/td><td>Travail Personnel de l\u2019Etudiant (TPE) Comp\u00e9tences \u00e9valu\u00e9es; Notions abord\u00e9es (\u00e0 mis parcours) dans les activit\u00e9s sous forme d\u2019exercices<\/td><td>10%<\/td><\/tr><tr><td>Semaine 5<\/td><td>Contr\u00f4le Continu (CC) Comp\u00e9tences \u00e9valu\u00e9es : Notions abord\u00e9es dans les activit\u00e9s sous forme d\u2019exercices<\/td><td>20%<\/td><\/tr><tr><td>Selon la programmation de l\u2019ISABEE<\/td><td>Examen de Session Normale (SN) et Session de Rattrapage Comp\u00e9tences \u00e9valu\u00e9es : Toutes les notions abord\u00e9es dans les activit\u00e9s<\/td><td>70%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>R\u00e8gles de fonctionnement du cours<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>#<\/strong><strong><\/strong><\/td><td><strong>Intitul\u00e9 de la r\u00e8gle<\/strong><\/td><td><strong>P\u00e9nalit\u00e9<\/strong><strong><\/strong><\/td><\/tr><tr><td>1<\/td><td>Respect des d\u00e9lais de remise des travaux<\/td><td>Retrait de quelques points selon la dur\u00e9e du retard<\/td><\/tr><tr><td>2<\/td><td>Absent\u00e9isme non justifi\u00e9 (appel obligatoire)<\/td><td>Interdiction de composer le CC<\/td><\/tr><tr><td>3<\/td><td>Travail personnel de l\u2019\u00e9tudiant (Devoir \u00e0 domicile \u00e0 faire obligatoirement)<\/td><td>Reprise plus d\u2019une fois<\/td><\/tr><tr><td>4<\/td><td>Plagiat<\/td><td>Remise \u00e0 l\u2019administration pour punition<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>#<\/strong><strong><\/strong><\/td><td><strong>Intitul\u00e9 de la r\u00e8gle<\/strong><\/td><td><strong>actions<\/strong><strong><\/strong><\/td><\/tr><tr><td>1<\/td><td>Participation aux cours<\/td><td>Points en plus accord\u00e9s<\/td><\/tr><tr><td>2<\/td><td>Bonne pr\u00e9sentation du cahier<\/td><td>Points en plus accord\u00e9s<\/td><\/tr><tr><td>3<\/td><td>Absences justifi\u00e9es<\/td><td>Heures d\u2019absence annul\u00e9es<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Bibliographie du cours et ressources compl\u00e9mentaires<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Walter Rudin <\/strong>\u2013 Principles of Mathematical Analysis (appel\u00e9 aussi Baby Rudin)\n<ol class=\"wp-block-list\">\n<li>Un livre rigoureux et bien structur\u00e9, adapt\u00e9 aux \u00e9tudiants souhaitant approfondir la th\u00e9orie de l\u2019analyse.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>Jean-Marie Monier <\/strong>\u2013 Analyse : cours et exercices corrig\u00e9s\n<ol class=\"wp-block-list\">\n<li>Un excellent livre en fran\u00e7ais qui couvre tout le programme d\u2019analyse avec des exercices corrig\u00e9s.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>Jean Dieudonn\u00e9 <\/strong>\u2013 Fondements de l&rsquo;Analyse Moderne\n<ol class=\"wp-block-list\">\n<li>Un ouvrage \u00e9crit par un grand math\u00e9maticien, destin\u00e9 aux \u00e9tudiants avanc\u00e9s.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>Terence Tao <\/strong>\u2013 Analysis I &amp; II\n<ol class=\"wp-block-list\">\n<li>Deux tomes qui expliquent l\u2019analyse de mani\u00e8re intuitive et rigoureuse, parfaits pour d\u00e9buter et approfondir.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>\u00c9lie Cartan <\/strong>\u2013 Cours d\u2019Analyse Math\u00e9matique\n<ol class=\"wp-block-list\">\n<li>Un livre fondamental qui pose les bases de l\u2019analyse avec une approche rigoureuse.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>Claude Brezinski <\/strong>\u2013 Analyse Math\u00e9matique : cours et exercices\n<ol class=\"wp-block-list\">\n<li>Livre d\u00e9taill\u00e9 avec de nombreux exercices pour tester ses connaissances.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>Serge Lang <\/strong>\u2013 A First Course in Calculus\n<ol class=\"wp-block-list\">\n<li>Une introduction claire au calcul diff\u00e9rentiel et int\u00e9gral avec des applications.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>Jean-Pierre Aubin <\/strong>\u2013 Analyse math\u00e9matique pour l\u2019ing\u00e9nieur<\/li>\n\n\n\n<li>Un livre orient\u00e9 vers les applications en ing\u00e9nierie et physique.<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Robert Bartle &amp; Donald Sherbert <\/strong>\u2013 Introduction to Real Analysis\n<ul class=\"wp-block-list\">\n<li>Un livre accessible qui introduit les bases de l\u2019analyse rigoureuse.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Nicolas Bourbaki <\/strong>\u2013 \u00c9l\u00e9ments d\u2019analyse<\/li>\n\n\n\n<li>Une r\u00e9f\u00e9rence tr\u00e8s th\u00e9orique pour ceux qui veulent approfondir.<\/li>\n\n\n\n<li><strong>Gilbert Strang <\/strong>\u2013 Calculus<\/li>\n\n\n\n<li>Un livre clair et p\u00e9dagogique, parfait pour une premi\u00e8re approche du calcul diff\u00e9rentiel et int\u00e9gral.<\/li>\n\n\n\n<li><strong>Richard Courant &amp; Fritz John <\/strong>\u2013 Introduction to Calculus and Analysis<\/li>\n\n\n\n<li>Un ouvrage bien illustr\u00e9 qui met en avant l\u2019intuition derri\u00e8re les concepts.<\/li>\n\n\n\n<li><strong>Jean-Fran\u00e7ois Dars, Annick Lesne, Yves Pomeau <\/strong>\u2013 M\u00e9thodes de math\u00e9matiques pour les sciences<\/li>\n\n\n\n<li>Un livre qui relie l\u2019analyse aux applications en physique et en sciences de l\u2019ing\u00e9nieur.<\/li>\n<\/ul>\n\n\n\n<p>14.&nbsp; MIT OpenCourseWare \u2013 Calculus &amp; Real Analysis<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Une ressource en ligne gratuite avec des vid\u00e9os et des notes de cours : <a href=\"https:\/\/ocw.mit.edu\/\">ocw.mit.edu<\/a><\/li>\n<\/ul>\n\n\n\n<p>15.&nbsp; Cours de l\u2019\u00c9cole Polytechnique (France)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Des notes de cours accessibles en ligne sur le site de l\u2019X : <a href=\"https:\/\/www.polytechnique.edu\/\">www.polytechnique.edu<\/a><\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fili\u00e8re et option : Sciences Fondamentales de Base et Appliqu\u00e9es (Tronc commun Scientifiques)&nbsp;; Niveau I Enseignant : Dr NOTUE KADJIE Arnaud Disponibilit\u00e9 :&nbsp;&nbsp; permanent &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Contact : Tel : 6 91 76 69 78 P\u00e9riode du cours : Semestre 1 (octobre- f\u00e9vrier) R\u00e9partition du volume horaire (CM : 30 heures. TD : 10 heures&nbsp;; TPE : [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-411","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.8 (Yoast SEO v27.6) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>INTRODUCTION A L\u2019ANALYSE ET A L\u2019ALGEBRE - SBA111 - Universit\u00e9 d&#039;Ebolowa<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/unv-ebolowa.cm\/index.php\/en\/2025\/09\/26\/introduction-a-lanalyse-et-a-lalgebre-sba111\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"INTRODUCTION A L\u2019ANALYSE ET A L\u2019ALGEBRE - SBA111\" \/>\n<meta property=\"og:description\" content=\"Fili\u00e8re et option : Sciences Fondamentales de Base et Appliqu\u00e9es (Tronc commun Scientifiques)&nbsp;; Niveau I Enseignant : Dr NOTUE KADJIE Arnaud Disponibilit\u00e9 :&nbsp;&nbsp; permanent &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Contact : Tel : 6 91 76 69 78 P\u00e9riode du cours : Semestre 1 (octobre- f\u00e9vrier) R\u00e9partition du volume horaire (CM : 30 heures. 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