{"id":113,"date":"2019-05-03T14:42:13","date_gmt":"2019-05-03T14:42:13","guid":{"rendered":"http:\/\/localhost\/?page_id=113"},"modified":"2019-06-17T13:44:37","modified_gmt":"2019-06-17T13:44:37","slug":"analise-i","status":"publish","type":"page","link":"http:\/\/localhost\/index.php\/ensino\/analise-i\/","title":{"rendered":"An\u00e1lise I"},"content":{"rendered":"<h2>An\u00e1lise I<\/h2>\n<h3>Informa\u00e7\u00f5es gerais sobre a disciplina<\/h3>\n<h4>(Primeiro semestre de 2019)<\/h4>\n<p><b>Hor\u00e1rio das aulas:<\/b>\u00a014:55-16:35, nas segundas, quartas e sextas.<br \/>\n<b>Sala:<\/b>\u00a02032, ICEx<br \/>\n<b>Professor:<\/b>\u00a0<a href=\"http:\/\/www.mat.ufmg.br\/~csaba\">Csaba Schneider<\/a><br \/>\n<b>Hor\u00e1rio da monitoria:<\/b>\u00a017-18:30 horas nas sextas<br \/>\n<b>Sala da monitoria:\u00a0<\/b>2073, ICEx<br \/>\n<b>Monitor:<\/b>\u00a0Lucas Resende<br \/>\n<b>Datas das provas:\u00a0<\/b><\/p>\n<h3>Programa<\/h3>\n<ul>\n<li>N\u00fameros Reais: axiom\u00e1tica, \u00eanfase na introdu\u00e7\u00e3o \u00e0 demonstra\u00e7\u00e3o; supremo e \u00ednfimo; aplica\u00e7\u00f5es elementares.<\/li>\n<li>Introdu\u00e7\u00e3o \u00e0 Topologia da reta: sequ\u00eancias (limites, monotonicidade, subsequ\u00eancia), sequ\u00eancias de Cauchy, Teorema de Bolzano-Weierstrass; abertos, fechados e compactos da reta.<\/li>\n<li>Fun\u00e7\u00f5es cont\u00ednuas: limites, continuidade, Teorema de valor intermedi\u00e1rio, Teorema de Weiestrass (extremos de fun\u00e7\u00f5es cont\u00ednuas em intervalos compactos).<\/li>\n<li>Derivadas: defini\u00e7\u00e3o, demonstra\u00e7\u00e3o das regras de deriva\u00e7\u00e3o; Teorema do valor m\u00e9dio e consequ\u00eancias; rela\u00e7\u00e3o entre fun\u00e7\u00f5es cont\u00ednuas e deriv\u00e1veis.<\/li>\n<li>Integra\u00e7\u00e3o: integrais inferior e superior, fun\u00e7\u00f5es integr\u00e1veis, integral como limite de somas de Riemann, primitivas, Teorema fundamental do c\u00e1lculo; Teorema da m\u00e9dia.<\/li>\n<li>F\u00f3rmula de Taylor com resto integral e outros restos.<\/li>\n<li>Regra de L&#8217;H\u00f4spital, logaritmo e exponencial.<\/li>\n<\/ul>\n<h3>Notas<\/h3>\n<ul>\n<li><a href=\"https:\/\/homepages.dcc.ufmg.br\/~lucasresenderc\/monitoria.html\">Notas por Lucas Resende<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/03\/teste-da-raiz-teste-da-rz\/\">Testes de converg\u00eancia para s\u00e9ries<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/06\/comutatividade-e-produto-de-series\/\">Comutatividade e produto de s\u00e9ries<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/06\/exercicios-series\/\">Exerc\u00edcios (s\u00e9ries)<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/08\/topologia-da-reta-conjuntos-abertos-e-fechados\/\">Topologia da reta: Conjuntos abertos e fechados<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/10\/topologia-da-reta-pontos-de-acumulacao-e-conjuntos-compactos\/\">Topologia da reta: Pontos de acumula\u00e7\u00e3o e conjuntos compactos<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/13\/exercicios-topologia\/\">Exerc\u00edcios (topologia)<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/13\/limite-de-funcoes\/\">Limite de fun\u00e7\u00f5es<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/20\/exercicios-limites-de-funcoes\/\">Exerc\u00edcios (limites de fun\u00e7\u00f5es)<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/20\/funcoes-continuas\/\">Fun\u00e7\u00f5es cont\u00ednuas<\/a><\/li>\n<li>Fun\u00e7\u00f5es cont\u00ednuas em intervalos<\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/29\/funcoes-continuas-sobre-conjuntos-compactos-e-funcoes-uniformemente-continuas\/\">Fun\u00e7\u00f5es cont\u00ednuas em conjuntos compactos e fun\u00e7\u00f5es uniformemente cont\u00ednuas<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/05\/31\/funcoes-derivaveis\/\">Fun\u00e7\u00f5es deriv\u00e1veis<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/06\/03\/funcoes-derivaveis-em-um-intervalo\/\">Fun\u00e7\u00f5es deriv\u00e1veis em um intervalo<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/06\/03\/a-formula-de-taylor\/\">A f\u00f3rmula de Taylor<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/06\/05\/exercicios-funcoes-continuas\/\">Exerc\u00edcios (fun\u00e7\u00f5es cont\u00ednuas)<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/06\/10\/exercicios-derivado\/\">Exerc\u00edcios (derivado)<\/a><\/li>\n<li><a href=\"http:\/\/localhost\/index.php\/2019\/06\/17\/exercicios-integral\/\">Exerc\u00edcios (integral)<\/a><\/li>\n<\/ul>\n<h3>Literatura principal<\/h3>\n<ul>\n<li>Terence Tao,\u00a0<i>Analysis &#8211; Volumes I-II<\/i>, Hindustan Book Agency, 2006.<\/li>\n<li>Elon Lages Lima,\u00a0<i>Curso de An\u00e1lise &#8211; Volume I<\/i>, Cole\u00e7\u00e3o Projeto Euclides, IMPA, 2002.<\/li>\n<\/ul>\n<h3>Outra literatura recomendada<\/h3>\n<ul>\n<li>Djairo Guedes de Figueiredo,\u00a0<i>An\u00e1lise I<\/i>, LTC, Grupo Gen, 1996.<\/li>\n<li>Michael Spivak,\u00a0<i>Calculus<\/i>, Publish or Perish, 2008.<\/li>\n<li>Serge Lang,\u00a0<i>Analysis I<\/i>, Addison-Wesley, 1968.<\/li>\n<li>Walter Rudin,\u00a0<i>Principles of Mathematical Analysis<\/i>, McGraw-Hill, 1976.<\/li>\n<\/ul>\n<h3>Outros recursos<\/h3>\n<ul>\n<li><a href=\"http:\/\/video.impa.br\/index.php?page=programa-de-verao-2011-analise-na-reta\">Videoaulas<\/a>\u00a0por Elon Lages Lima no Programa de Ver\u00e3o do IMPA.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>An\u00e1lise I Informa\u00e7\u00f5es gerais sobre a disciplina (Primeiro semestre de 2019) Hor\u00e1rio das aulas:\u00a014:55-16:35, nas segundas, quartas e sextas. Sala:\u00a02032, ICEx Professor:\u00a0Csaba Schneider Hor\u00e1rio da monitoria:\u00a017-18:30 horas nas sextas Sala da monitoria:\u00a02073, ICEx Monitor:\u00a0Lucas Resende Datas das provas:\u00a0 Programa N\u00fameros Reais: axiom\u00e1tica, \u00eanfase na introdu\u00e7\u00e3o \u00e0 demonstra\u00e7\u00e3o; supremo e \u00ednfimo; aplica\u00e7\u00f5es elementares. Introdu\u00e7\u00e3o \u00e0 Topologia &hellip; <a href=\"http:\/\/localhost\/index.php\/ensino\/analise-i\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">An\u00e1lise I<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":64,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/113"}],"collection":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/comments?post=113"}],"version-history":[{"count":18,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/113\/revisions"}],"predecessor-version":[{"id":292,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/113\/revisions\/292"}],"up":[{"embeddable":true,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/64"}],"wp:attachment":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/media?parent=113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}