{"id":31850,"date":"2024-01-08T11:32:36","date_gmt":"2024-01-08T09:32:36","guid":{"rendered":"https:\/\/www.cpge-brizeux.fr\/wordpress\/?p=31850"},"modified":"2024-01-15T12:29:14","modified_gmt":"2024-01-15T10:29:14","slug":"semaine-15-du-08-01-2024","status":"publish","type":"post","link":"https:\/\/www.cpge-brizeux.fr\/wordpress\/pc\/mathematiques-pc-2324\/semaine-15-du-08-01-2024.html","title":{"rendered":"Semaine 15 du 08\/01\/2024"},"content":{"rendered":"
\n

Programme de colles de la semaine du 15\/01 : 14_prog_DSE_probas<\/a>
\n<\/span><\/big><\/b><\/p>\n<\/div>\n

Chapitre IX S\u00e9ries enti\u00e8res :<\/span>
\n<\/strong>Notion de s\u00e9rie enti\u00e8re de la variable complexe. Notation, lien avec les s\u00e9ries num\u00e9riques. Exemples. S\u00e9rie enti\u00e8re g\u00e9om\u00e9trique. S\u00e9rie enti\u00e8re exponentielle. Lemme d’Abel. Rayon de convergence. Somme d’une s\u00e9rie enti\u00e8re sur le disque ouvert de convergence.
\nD\u00e9termination directe du rayon de convergence \u00e0 partir de valeurs de convergence ou de divergence.
\nR\u00e8gle de d’Alembert des s\u00e9ries enti\u00e8res.
\n<\/em>exercice(s) : 1,15,18
\n<\/em><\/span><\/p>\n
\n

\\[latex R(\\sum a_n z^n)=R(\\sum n a_n z^n)\\]<\/span><\/p>\n

exercice(s) : 5, 8<\/span><\/p>\n

\n

S\u00e9rie enti\u00e8re de la variable r\u00e9elle. Convergence normale sur tout segment de l’intervalle ouvert de convergence.<\/span>
\nContinuit\u00e9 de la somme d’une s\u00e9rie enti\u00e8re sur l’ouvert de convergence. D\u00e9rivation terme \u00e0 terme, classe $C^\\infty$<\/span><\/p>\n

exercice(s) : 10 (\u00e0 finir pour vendredi)
\n<\/span><\/p>\n

\n

Fonctions d\u00e9veloppables en s\u00e9ries enti\u00e8res. Unicit\u00e9 du DSE.
\nexercice(s) : 10 (fin)
\n<\/span><\/p>\n<\/div>\n

\n

Document de cours :ch09_Cours_Ser_Ent_2023<\/a><\/p>\n

Documents distribu\u00e9s :<\/span><\/big><\/b><\/big><\/b><\/p>\n

TD : ch09_TD_Ser_Ent_2023<\/a><\/span><\/big><\/b><\/p>\n

Devoirs : <\/strong><\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Programme de colles de la semaine du 15\/01 : 14_prog_DSE_probas Chapitre IX S\u00e9ries enti\u00e8res : Notion de s\u00e9rie enti\u00e8re de la variable complexe. Notation, lien avec les s\u00e9ries num\u00e9riques. Exemples. S\u00e9rie enti\u00e8re g\u00e9om\u00e9trique. S\u00e9rie enti\u00e8re exponentielle. Lemme d’Abel. Rayon de…<\/p>\n

Read more →<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[362],"tags":[],"class_list":["post-31850","post","type-post","status-publish","format-standard","hentry","category-mathematiques-pc-2324"],"_links":{"self":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/31850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/comments?post=31850"}],"version-history":[{"count":7,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/31850\/revisions"}],"predecessor-version":[{"id":31880,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/31850\/revisions\/31880"}],"wp:attachment":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/media?parent=31850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/categories?post=31850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/tags?post=31850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}