{"id":26785,"date":"2022-01-04T08:18:07","date_gmt":"2022-01-04T08:18:07","guid":{"rendered":"https:\/\/www.cpge-brizeux.fr\/wordpress\/?p=26785"},"modified":"2022-01-06T12:37:51","modified_gmt":"2022-01-06T12:37:51","slug":"26785","status":"publish","type":"post","link":"https:\/\/www.cpge-brizeux.fr\/wordpress\/pc\/mathematiques-pc-2122\/26785.html","title":{"rendered":"Semaine 15 du 03 au 07\/01\/2022"},"content":{"rendered":"
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Programme de colles de la semaine \u00e0 venir<\/span><\/big><\/b><\/p>\n

programme de colles de la semaine de la rentr\u00e9e du 10\/01\/2022 : 13_prog_probas_DSE<\/a>
\n<\/strong><\/span><\/p>\n<\/div>\n

Chapitre X : S\u00e9ries enti\u00e8res<\/strong><\/span>
\nS\u00e9ries enti\u00e8res de la variable complexe. D\u00e9finition, Rayon de convergence. Lemme d’abel, disque ouvert de convergence. S\u00e9rie enti\u00e8re g\u00e9om\u00e9trique, s\u00e9rie enti\u00e8re exponentielle. D\u00e9termination du rayon de convergence par comparaison (grand O, \u00e9quivalent, majoration du module), utilisation de la r\u00e8gle de d’Alembert des s\u00e9ries num\u00e9riques, m\u00e9thode directe \u00e0 l’aide de valeurs de convergence ou de divergence via encadrements.
\n<\/span>exercice(s) 1a, 1c, 1d, 2, 11, 17
\n<\/em><\/span><\/p>\n
\n

Le rayon de convergence de $\\sum na_n z^n$ est celui de $\\sum a_n z^n$ .<\/span><\/p>\n

S\u00e9ries enti\u00e8res de la variable r\u00e9elle, intervalle ouvert de convergence. Fonction d\u00e9veloppable en s\u00e9rie enti\u00e8re.
\n<\/span><\/p>\n

exercice(s) 18, 9, 16
\n<\/span><\/em><\/span><\/p>\n

\n

Convergence normale sur les segments de l’ouvert de convergence. Continuit\u00e9 de la somme d’une s\u00e9rie enti\u00e8re (de la variable r\u00e9elle). Int\u00e9gration terme \u00e0 terme.
\n<\/span><\/p>\n

exercice(s) 3, 6a, 20.1 (\u00e0 finir)
\n<\/em><\/span><\/p>\n

 <\/p>\n

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D\u00e9rivation terme \u00e0 terme.<\/span><\/p>\n

exercice(s) 20, 6b, 6c<\/em><\/span><\/p>\n<\/div>\n

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

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

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

DM8 : dm08_probas<\/a><\/span><\/big><\/b><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Programme de colles de la semaine \u00e0 venir programme de colles de la semaine de la rentr\u00e9e du 10\/01\/2022 : 13_prog_probas_DSE Chapitre X : S\u00e9ries enti\u00e8res S\u00e9ries enti\u00e8res de la variable complexe. D\u00e9finition, Rayon de convergence. Lemme d’abel, disque ouvert…<\/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":[317],"tags":[],"class_list":["post-26785","post","type-post","status-publish","format-standard","hentry","category-mathematiques-pc-2122"],"_links":{"self":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/26785","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=26785"}],"version-history":[{"count":6,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/26785\/revisions"}],"predecessor-version":[{"id":26800,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/26785\/revisions\/26800"}],"wp:attachment":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/media?parent=26785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/categories?post=26785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/tags?post=26785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}