{"id":3815,"date":"2025-04-14T20:14:22","date_gmt":"2025-04-14T23:14:22","guid":{"rendered":"https:\/\/wp.ufpel.edu.br\/zahn\/?page_id=3815"},"modified":"2025-04-14T20:15:31","modified_gmt":"2025-04-14T23:15:31","slug":"mmxxiv-2","status":"publish","type":"page","link":"https:\/\/wp.ufpel.edu.br\/zahn\/disciplinas\/mmxxiv-2\/","title":{"rendered":"MMXXIV"},"content":{"rendered":"<p style=\"text-align: center;\"><strong>Ano de 2024 de Nosso Senhor<\/strong><!--more--><\/p>\n<p style=\"text-align: center;\"><strong>Segundo Semestre de MMXXIV<\/strong><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\"><strong>C\u00e1lculo I (Matem\u00e1tica diurno)<\/strong><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3539 aligncenter\" src=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/NewtonXLeibniz-318x318.webp\" alt=\"\" width=\"271\" height=\"271\" srcset=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/NewtonXLeibniz-318x318.webp 318w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/NewtonXLeibniz-159x159.webp 159w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/NewtonXLeibniz-768x768.webp 768w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/NewtonXLeibniz-619x619.webp 619w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/NewtonXLeibniz.webp 1024w\" sizes=\"auto, (max-width: 271px) 100vw, 271px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 10pt;\">UQuem inventou o C\u00e1lculo? Newton ou<\/span><span style=\"font-size: 10pt;\"> Leibniz? Um eterno duelo entre gigantes, ambientalizado no \u00a0Universo Star Wars.<\/span><\/p>\n<p>Nesta disciplina estudaremos o C\u00e1lculo Diferencial a uma vari\u00e1vel real. Mais precisamente, estudaremos limites, continuidade e diferenciabilidade, bem como suas aplica\u00e7\u00f5es.<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #333399;\">Plano de ensino<\/span><\/strong><\/p>\n<p>Uma c\u00f3pia pdf do plano de ensino pode ser baixada, clicando <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2023\/04\/plano_ensino_2024_2_11100080_T2.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/p>\n<p>As aulas ocorrer\u00e3o na sala 209 do pr\u00e9dio 5, no Campus Cap\u00e3o do Le\u00e3o.<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #333399;\">Datas das provas (Dies ir\u00e6, dies illa)<\/span><\/strong><\/p>\n<p style=\"text-align: center;\">Prova 01:-<em> III &#8211; II &#8211; MMXXV &#8211; \u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Gabarito-c1.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/em><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/Prova_02.pdf\" target=\"_blank\" rel=\"noopener\">Prova 02<\/a>: <em>V &#8211; III &#8211; MMXXV &#8211; <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/Gab_Prova_02.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/em><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/Prova_03.pdf\" target=\"_blank\" rel=\"noopener\">Prova 03<\/a>: <em>XXVIII &#8211; III &#8211; MMXXV &#8211; <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/Gab_Prv_03.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/em><\/p>\n<p style=\"text-align: center;\">Exame: <em>II &#8211; IV &#8211; MMXXV<\/em><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #000080;\">Listas de exerc\u00edcios<\/span><\/strong><\/p>\n<ul>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/lista_01.pdf\" target=\"_blank\" rel=\"noopener\">Lista 01<\/a> &#8211; Composi\u00e7\u00e3o de fun\u00e7\u00f5es, inventividade, sobrejetividade, bijetividade. Fun\u00e7\u00f5es inversas.<\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/lista_02.pdf\" target=\"_blank\" rel=\"noopener\">Lista 02<\/a> &#8211; Fun\u00e7\u00f5es hiperb\u00f3licas. No\u00e7\u00f5es de Topologia. Limites de fun\u00e7\u00f5es.\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/Resp-c1-L-2.pdf\" target=\"_blank\" rel=\"noopener\">Resolu\u00e7\u00f5es <\/a><\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/lista_03.pdf\" target=\"_blank\" rel=\"noopener\">Lista 03<\/a> &#8211; Limites: propriedades, c\u00e1lculos, limites laterais, Teorema do Sandu\u00edche.<\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/lista_04.pdf\" target=\"_blank\" rel=\"noopener\">Lista 04<\/a> &#8211; C\u00e1lculos de limites. Limites not\u00e1veis. Limites infinitos e no infinito.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/lista_05.pdf\" target=\"_blank\" rel=\"noopener\">Lista 05<\/a> &#8211; Fun\u00e7\u00f5es cont\u00ednuas.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/lista_06.pdf\" target=\"_blank\" rel=\"noopener\">Lista 06<\/a> &#8211; Derivadas (primeiros conceitos)<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/lista_07.pdf\" target=\"_blank\" rel=\"noopener\">Lista 07<\/a> &#8211; Regras de deriva\u00e7\u00e3o. Deriva\u00e7\u00e3o impl\u00edcita e de fun\u00e7\u00f5es definidas parametricamente. Regra da cadeia.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/lista_08.pdf\" target=\"_blank\" rel=\"noopener\">Lista 08<\/a> &#8211; Diferenciais.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/lista-09.pdf\" target=\"_blank\" rel=\"noopener\">Lista 09<\/a> &#8211; Taxas relacionadas.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/lista_10.pdf\" target=\"_blank\" rel=\"noopener\">Lista 10<\/a> &#8211; Teoremas de Rolle e de Lagrange<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/lista_11.pdf\" target=\"_blank\" rel=\"noopener\">Lista 11<\/a> &#8211; Problemas de m\u00e1ximos e m\u00ednimos<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/lista_12.pdf\" target=\"_blank\" rel=\"noopener\">Lista 12<\/a> &#8211; Regra de L&#8217;Hopital. Miscel\u00e2nea de exerc\u00edcios.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><strong>C\u00e1lculo on-line de derivadas<\/strong><\/p>\n<p>clique <a href=\"https:\/\/www.derivative-calculator.net\/\" target=\"_blank\" rel=\"noopener\">aqui <\/a>para acessar a p\u00e1gina da calculadora de derivadas on-line. \u00c9 interessante, pois mostra os passos.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #333399;\"><strong>Arquivos pdf das aulas<\/strong><\/span><\/p>\n<p>\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/C1a1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 01<\/a> (11\/11\/24) &#8211; Apresenta\u00e7\u00e3o da disciplina. Composi\u00e7\u00e3o de fun\u00e7\u00f5es e propriedades. Injetiviodade, sobrejetividade e bijetividade.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/C1a2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 02 <\/a>\u00a0(13\/11\/24) &#8211; Fun\u00e7\u00f5es inversas. Fun\u00e7\u00f5es hiperb\u00f3licas diretas: seno hiperb\u00f3lico e cosseno hiperb\u00f3lico.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/C1a3.pdf\" target=\"_blank\" rel=\"noopener\">Aula 03<\/a> (18\/11\/24) &#8211; Fun\u00e7\u00f5es hiperb\u00f3licas diretas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/C1a4.pdf\" target=\"_blank\" rel=\"noopener\">Aula 04<\/a>\u00a0(22\/11\/24) &#8211; Fun\u00e7\u00f5es hiperb\u00f3licas inversas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/C1a5.pdf\" target=\"_blank\" rel=\"noopener\">Aula 05<\/a> (25\/11\/24) &#8211; Aula de exerc\u00edcios sobre a Lista 01. Dedu\u00e7\u00e3o de algumas f\u00f3rmulas da trigonometria hiperb\u00f3lica. (Aula gravada no e-aula).<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/1a6.pdf\" target=\"_blank\" rel=\"noopener\">Aula 06<\/a>\u00a0 (02\/12\/24) &#8211; No\u00e7\u00f5es de topologia: interior de um conjunto. Abertos de R. Ponto de acumula\u00e7\u00e3o de um conjunto. Conceito de limite de fun\u00e7\u00e3o de uma vari\u00e1vel real.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/C1a7.pdf\" target=\"_blank\" rel=\"noopener\">Aula 07<\/a>\u00a0 (04\/12\/24) &#8211; Exemplos de c\u00e1lculo de limite atrav\u00e9s da defini\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/C1a8.pdf\" target=\"_blank\" rel=\"noopener\">Aula 08<\/a>\u00a0(06\/12\/24) &#8211; Unicidade do limite. Teorema do Sandu\u00edche. Propriedades aritm\u00e9ticas dos limites.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/C1a9.pdf\" target=\"_blank\" rel=\"noopener\">Aula 09<\/a> (09\/12\/24) &#8211; Indetermina\u00e7\u00e3o da forma 0\/0 para fun\u00e7\u00f5es racionais e irracionais. Limites laterais.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/C1a10.pdf\" target=\"_blank\" rel=\"noopener\">Aula 10<\/a>\u00a0 (11\/12\/24) &#8211; Limites no infinito e limites infinitos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/C1a11.pdf\" target=\"_blank\" rel=\"noopener\">Aula 11<\/a>\u00a0(16\/12\/24) &#8211; Gr\u00e1fico de fun\u00e7\u00f5es com aux\u00edlio de limites laterais, infinitos e no infinito. Primeiro limite not\u00e1vel (limite trigonom\u00e9trico fundamental)<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/C1A12.pdf\" target=\"_blank\" rel=\"noopener\">Aula 12<\/a>\u00a0 (18\/12\/24) &#8211; Consequ\u00eancias do primeiro limite not\u00e1vel. O segundo limite not\u00e1vel.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/C1a13.pdf\" target=\"_blank\" rel=\"noopener\">Aula 13<\/a>\u00a0 (20\/12\/24) &#8211; Outro exemplo de uso do segundo limite not\u00e1vel. Resolu\u00e7\u00e3o de exerc\u00edcios da lista 03.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/Resp-c1-L-2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 14<\/a> (17\/01\/25) &#8211; Resolu\u00e7\u00e3o de algumas quest\u00f5es da lista 02. [estudo em casa]<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/C1-resol-L-4.pdf\" target=\"_blank\" rel=\"noopener\">Aula 15<\/a> (22\/01\/25) &#8211; Resolu\u00e7\u00e3o de algumas quest\u00f5es da lista 04 [estudo em casa]<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/C1a16.pdf\" target=\"_blank\" rel=\"noopener\">Aula 16<\/a>\u00a0(27\/01\/25) &#8211; Aula de exerc\u00edcios, das listas 4 e 3.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/C1A17.pdf\" target=\"_blank\" rel=\"noopener\">Aula 17<\/a>\u00a0 (29\/01\/25) &#8211; Continuidade. Fun\u00e7\u00f5es cont\u00ednuas e propriedades da continuidade.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/C1a18.pdf\" target=\"_blank\" rel=\"noopener\">Aula 18<\/a> (31\/01\/25) &#8211; Aula de exerc\u00edcios, contemplando revis\u00e3o sobre defini\u00e7\u00e3o de limite.<\/p>\n<p>Aula 19 (03\/02\/25) &#8211; Aplica\u00e7\u00e3o da Prova 01.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1a20.pdf\" target=\"_blank\" rel=\"noopener\">Aula 20<\/a> (05\/02\/25) &#8211; Fun\u00e7\u00f5es cont\u00ednuas, uma revis\u00e3o. Fun\u00e7\u00f5es cont\u00ednuas em intervalos: teoremas do valor intermedi\u00e1rio e de Weierstrass.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/c1a20.pdf\" target=\"_blank\" rel=\"noopener\">Aula 21<\/a>\u00a0(07\/02\/25) &#8211; Derivadas: conceito e significado geom\u00e9trico. Reta tangente em uma fun\u00e7\u00e3o. Fun\u00e7\u00e3o derivada e c\u00e1lculo pela defini\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1a22.pdf\" target=\"_blank\" rel=\"noopener\">Aula 22<\/a>\u00a0 (10\/02\/25) &#8211; Revis\u00e3o do conceito de derivada. O Significado f\u00edsico da derivada. Derivadas laterais.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1-a-23.pdf\" target=\"_blank\" rel=\"noopener\">Aula 23<\/a>\u00a0 (12\/02\/25) \u00a0&#8211; Primeiras regras de deriva\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/c1a24.pdf\" target=\"_blank\" rel=\"noopener\">Aula 24<\/a>\u00a0 (14\/02\/25) &#8211; Outras regras de deriva\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/c1a25.pdf\" target=\"_blank\" rel=\"noopener\">Aula 25<\/a> (15\/02\/25) &#8211; V\u00e1rios exemplos de c\u00e1lculos de derivadas. Derivadas das fun\u00e7\u00f5es hiperb\u00f3licas diretas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1a26.pdf\" target=\"_blank\" rel=\"noopener\">Aula 26<\/a>\u00a0 (17\/02\/25) &#8211; \u00a0Outros exemplos de c\u00e1lculo de derivadas. A derivada como aproxima\u00e7\u00e3o linear. Diferencial de uma fun\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1a27.pdf\" target=\"_blank\" rel=\"noopener\">Aula 27<\/a>\u00a0(19\/02\/25) &#8211; Mais sobre diferenciabilidade. O teorema da regra da cadeia. Derivadas de fun\u00e7\u00f5es definida implicitamente.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/c1a28.pdf\" target=\"_blank\" rel=\"noopener\">Aula 28<\/a> (21\/02\/25) &#8211; Nota\u00e7\u00f5es da derivada, como quociente diferencial. Derivadas das fun\u00e7\u00f5es trigonom\u00e9tricas inversas. Derivadas de fun\u00e7\u00f5es definidas parametricamente.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1a29.pdf\" target=\"_blank\" rel=\"noopener\">Aula 29<\/a>\u00a0 (24\/02\/25) &#8211; Taxas relacionadas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gama1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 30<\/a> (25\/02\/25) &#8211; Taxas relacionadas (resolu\u00e7\u00e3o de exerc\u00edcios da Lista 09)[ass\u00edncrono]. O v\u00eddeo da aula pode ser acessado <a href=\"https:\/\/www.youtube.com\/watch?v=3vUwMh9yjTU\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gama2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 31<\/a> (25\/02\/25) Taxas relacionadas (resolu\u00e7\u00e3o de exerc\u00edcios da Lista 09, parte 02)[ass\u00edncrono]. O v\u00eddeo da aula pode ser acessado <a href=\"https:\/\/www.youtube.com\/watch?v=6ufoWaCpA0o\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1a32.pdf\" target=\"_blank\" rel=\"noopener\">Aula 32<\/a>\u00a0 (26\/02\/25) &#8211; Aula de exerc\u00edcios, sobre a lista 07. Derivadas de ordem superior.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/C1a33.pdf\" target=\"_blank\" rel=\"noopener\">Aula 33<\/a> (28\/02\/25) &#8211; Aula de exerc\u00edcios, sobre a resolu\u00e7\u00e3o da lista 05.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/C1a34.pdf\" target=\"_blank\" rel=\"noopener\">Aula 34<\/a>\u00a0(07\/03\/25) &#8211; Aula de exerc\u00edcios.<\/p>\n<p>Aula 35 (10\/03\/25) &#8211; Aplica\u00e7\u00e3o da Prova 02.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/C1a36.pdf\" target=\"_blank\" rel=\"noopener\">Aula 36<\/a>\u00a0 (12\/03\/25) &#8211; Extremos relativos e absolutos. Pontos cr\u00edticos. Teoremas de Rolle e de Lagrange(T.V.M)<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/C1a38.pdf\" target=\"_blank\" rel=\"noopener\">Aula 37<\/a> \u00a0(14\/03\/25) &#8211; Consequ\u00eancias do Teorema de Lagrange. Intervalos de crescimento e decrescimento de uma fun\u00e7\u00e3o. Determina\u00e7\u00e3o de pontos m\u00e1ximo e m\u00ednimo de uma fun\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/C1a38-1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 38<\/a>\u00a0 (17\/03\/25) &#8211; Problemas envolvendo m\u00e1ximos e m\u00ednimos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/C1-a39.pdf\" target=\"_blank\" rel=\"noopener\">Aula 39<\/a> (19\/03\/25)- Concavidade e ponto de inflex\u00e3o. Esbo\u00e7o gr\u00e1fico de fun\u00e7\u00f5es, via um estudo completo.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/c1a40-.pdf\" target=\"_blank\" rel=\"noopener\">Aula 40<\/a>\u00a0 (21\/03\/25) &#8211; Outros exemplos de esbo\u00e7o gr\u00e1fico mediante an\u00e1lise completa. Regra de L\u2019Hopital.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/C1A41.pdf\" target=\"_blank\" rel=\"noopener\">Aula 41<\/a>\u00a0(24\/03\/25) &#8211; Aula de exerc\u00edcios.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/C1a42.pdf\" target=\"_blank\" rel=\"noopener\">Aula 42<\/a> (26\/03\/25) &#8211; Aula de exerc\u00edcios ( resolu\u00e7\u00e3o de quest\u00f5es da lista 12)<\/p>\n<p style=\"text-align: center;\">##########################################<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #0000ff;\">Aritm\u00e9tica (Matem\u00e1tica diurno)<\/span><\/strong><\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3540 alignnone\" src=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gauss-318x318.webp\" alt=\"\" width=\"269\" height=\"269\" srcset=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gauss-318x318.webp 318w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gauss-159x159.webp 159w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gauss-768x768.webp 768w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gauss-619x619.webp 619w, https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gauss.webp 1024w\" sizes=\"auto, (max-width: 269px) 100vw, 269px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 10pt;\">Gauss trabalhando com a Aritm\u00e9tica<\/span><\/p>\n<p>Nesta disciplina estudaremos o conjunto dos n\u00fameros inteiros, dando uma aten\u00e7\u00e3o especial ao princ\u00edpio da indu\u00e7\u00e3o matem\u00e1tica, divisibilidade de inteiros e o algoritmo da divis\u00e3o de Euclides, m\u00e1ximo divisor comum e m\u00ednimo m\u00faltiplo comum, Congru\u00eancias, teorema fundamental da aritm\u00e9tica e equa\u00e7\u00f5es diofantinas.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #333399;\">Plano de ensino<\/span><\/strong><\/p>\n<p style=\"text-align: center;\">Uma c\u00f3pia pdf do plano pode ser baixada, clicando <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2023\/04\/plano_ensino_2024_2_11100082_T1-2.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/p>\n<p>As aulas ocorrer\u00e3o na sala 110 do pr\u00e9dio 16, no Campus Cap\u00e3o do Le\u00e3o.<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #333399;\"><strong>Datas das provas <em>(Dum veneris s\u00e6culum per ignem<\/em>)<\/strong><\/span><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/PRV01.pdf\" target=\"_blank\" rel=\"noopener\">Prova 01<\/a>: \u00a0<em>XXXI &#8211; I &#8211; MMXXV &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Gab-aritm.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito <\/a><\/em><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/PRV02.pdf\" target=\"_blank\" rel=\"noopener\">Prova 02<\/a>: \u00a0<em>XXVIII &#8211; III &#8211; MMXXV &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/PRV02-gab.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/em><\/p>\n<p style=\"text-align: center;\">Optativa: <em> II &#8211; IV &#8211; MMXXV<\/em><\/p>\n<p style=\"text-align: center;\">Exame:<em> IV &#8211; IV &#8211; MMXXV<\/em><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #333399;\"><strong>Listas de Exerc\u00edcios<\/strong><\/span><\/p>\n<ul>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/L_01.pdf\" target=\"_blank\" rel=\"noopener\">Lista 01<\/a> &#8211; Hist\u00f3rico, origens do processo de contagem, bases e sistemas de numera\u00e7\u00e3o. N\u00fameros figurados.<\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/L_02.pdf\" target=\"_blank\" rel=\"noopener\">Lista 02<\/a> &#8211; O conjunto dos n\u00fameros naturais e os axiomas de Peano.<\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/L_03.pdf\" target=\"_blank\" rel=\"noopener\">Lista 03<\/a> &#8211; O conjunto dos n\u00fameros inteiros.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/L_04.pdf\" target=\"_blank\" rel=\"noopener\">Lista 04<\/a> &#8211; N\u00fameros binomiais e bin\u00f4mio de Newton. M\u00faltiplos e divisores.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/L_05.pdf\" target=\"_blank\" rel=\"noopener\">Lista 05<\/a> &#8211; Sistemas de base b. M\u00e1ximo divisor comum.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/L_06.pdf\" target=\"_blank\" rel=\"noopener\">Lista 06<\/a> &#8211; N\u00fameros primos e o Teorema Fundamental da Aritm\u00e9tica.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/L_07.pdf\" target=\"_blank\" rel=\"noopener\">Lista 07<\/a> &#8211; Congru\u00eancias.<\/li>\n<li><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/L_08.pdf\" target=\"_blank\" rel=\"noopener\">Lista 08<\/a> &#8211; Inteiros m\u00f3dulo m.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><span style=\"color: #333399;\"><strong>Materiais adicionais, et cetera<\/strong><\/span><\/p>\n<ul>\n<li>Artigo versando sobre &#8220;paleoevid\u00eancia do conceito de n\u00famero no paleo\u00edtico m\u00e9dio&#8221;, do autor \u00a0Manoel de Campos Almeida. Acesso <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/PALEOEVIDNCIADEEMPREGODOCONCEITODENUMERONOPALEOLIRG.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/li>\n<li>Um texto sobre n\u00fameros figurados, acesso <a href=\"https:\/\/www.methodist.edu\/wp-content\/uploads\/2022\/06\/mr2018_shane.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/li>\n<li>A resolu\u00e7\u00e3o de um exerc\u00edcio de indu\u00e7\u00e3o da lista 03 pode ser baixada\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/L3e6.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a><\/li>\n<\/ul>\n<p style=\"text-align: center;\"><strong><span style=\"color: #333399;\">Arquivos pdf das aulas<\/span><\/strong><\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/Aa1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 01<\/a>\u00a0 (13\/11\/24) &#8211; Apresenta\u00e7\u00e3o da disciplina. Origens dos n\u00fameros e do processo de contagem. Contagem do homem primitivo. Sistemas de numera\u00e7\u00e3o eg\u00edpcio e babil\u00f4nico.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/Aa2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 02<\/a>\u00a0 (22\/11\/24) &#8211; Sistemas romano e grego. Sistema posicional. Os gregos e a Matem\u00e1tica. Pitagoras. N\u00fameros figurados.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/11\/Aa3.pdf\" target=\"_blank\" rel=\"noopener\">Aula 03<\/a>\u00a0 (27\/11\/24) &#8211; Mais sobre n\u00fameros figurados. Ternos Pitag\u00f3ricos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/Aa4.pdf\" target=\"_blank\" rel=\"noopener\">Aula 04<\/a> (04\/12\/24) &#8211; \u00a0O conjunto dos n\u00fameros naturais atrav\u00e9s dos axiomas de Peano. Princ\u00edpio da indu\u00e7\u00e3o matem\u00e1tica, no primeiro formato.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/Aak.pdf\" target=\"_blank\" rel=\"noopener\">Aula 05<\/a> (06\/12\/24) &#8211; \u00a0Adi\u00e7\u00e3o e multiplica\u00e7\u00e3o em N e propriedades, via axiomas de Peano.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/Aa6.pdf\" target=\"_blank\" rel=\"noopener\">Aula 06 <\/a> (11\/12\/24) &#8211; O conjunto dos n\u00fameros inteiros e seus axiomas. Propriedades.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/Aa7.pdf\" target=\"_blank\" rel=\"noopener\">Aula 07<\/a> (18\/12\/24) &#8211; \u00a0Rela\u00e7\u00e3o de ordem em Z. Conjuntos limitados inferiormente em Z e o princ\u00edpio da boa ordem.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/12\/Aa08.pdf\" target=\"_blank\" rel=\"noopener\">Aula 08<\/a>\u00a0 (20\/12\/24) &#8211; Princ\u00edpio da indu\u00e7\u00e3o matem\u00e1tica.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/resol-L-2-aritm.pdf\" target=\"_blank\" rel=\"noopener\">Aula 09<\/a>\u00a0 \u00a0(21\/01\/25) &#8211; Resolu\u00e7\u00e3o de exerc\u00edcios da lista 02 para estudo em casa.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/Aa10.pdf\" target=\"_blank\" rel=\"noopener\">Aula 10<\/a>\u00a0 (29\/01\/25) &#8211; Aula de exerc\u00edcios. Resolu\u00e7\u00e3o de quest\u00f5es da Lista 03.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/Aa11.pdf\" target=\"_blank\" rel=\"noopener\">Aula 11<\/a> (30\/01\/25) &#8211; Aula extra de exerc\u00edcios sobre indu\u00e7\u00e3o matem\u00e1tica, das listas 02 e 03.[estudo ass\u00edncrono]<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/01\/PRV01.pdf\" target=\"_blank\" rel=\"noopener\">Aula 12<\/a> (31\/01\/25) &#8211; Realiza\u00e7\u00e3o da Prova 01.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Aa13.pdf\" target=\"_blank\" rel=\"noopener\">Aula 13<\/a> (05\/02\/25) &#8211; N\u00fameros binomiais e teorema do bin\u00f4mio de Newton.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Aa14.pdf\" target=\"_blank\" rel=\"noopener\">Aula 14<\/a>\u00a0 (07\/02\/25) &#8211; M\u00faltiplos e divisores e o algoritmo da divis\u00e3o de Euclides.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/aa15.pdf\" target=\"_blank\" rel=\"noopener\">Aula 15<\/a>\u00a0 (12\/02\/25) &#8211; Aplica\u00e7\u00e3o do algoritmo de Euclides. Sistema de numera\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/aa16.pdf\" target=\"_blank\" rel=\"noopener\">Aula 16<\/a> (14\/02\/25) &#8211; Ideais em Z. M\u00e1ximo divisor comum. Teorema de B\u00e9zout.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Aa17.pdf\" target=\"_blank\" rel=\"noopener\">Aula 17<\/a>\u00a0 (19\/02\/25) &#8211; propriedades do mdc. Algoritmo de Euclides para c\u00e1lculo do m\u00e1ximo divisor comum.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/aa18.pdf\" target=\"_blank\" rel=\"noopener\">Aula 18<\/a>\u00a0 (21\/02\/25) &#8211; N\u00fameros primos. Teorema de Euclides. Crivo de Erast\u00f3stenes.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Aa19.pdf\" target=\"_blank\" rel=\"noopener\">Aula 19<\/a> (24\/02\/25) &#8211; M\u00ednimo m\u00faltiplo comum [para estudo ass\u00edncrono].<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Aa20.pdf\" target=\"_blank\" rel=\"noopener\">Aula 20<\/a> (26\/02\/25) &#8211; O teorema fundamental da aritm\u00e9tica e consequ\u00eancias.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/02\/Aa21.pdf\" target=\"_blank\" rel=\"noopener\">Aula 21<\/a> (28\/02\/25) &#8211; Congru\u00eancia m\u00f3dulo m.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/aa22.pdf\" target=\"_blank\" rel=\"noopener\">Aula 22<\/a>\u00a0 (07\/03\/25) &#8211; Aula de exerc\u00edcios, das listas 04 e 05.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/Aa23.pdf\" target=\"_blank\" rel=\"noopener\">Aula 23<\/a>\u00a0(12\/03\/25) &#8211; Fun\u00e7\u00e3o de Euler. Teorema de Euler e o pequeno Teorema de Fermat.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/Aa24.pdf\" target=\"_blank\" rel=\"noopener\">Aula 24<\/a>\u00a0 (14\/03\/25) &#8211; Um exemplo de uso do pequeno Teorema de Fermat. Inteiros m\u00f3dulo m. Adi\u00e7\u00e3o e produto em Zm.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/aa25.pdf\" target=\"_blank\" rel=\"noopener\">Aula 25<\/a>\u00a0 (19\/03\/25) &#8211; Zm como um anel comutativo. Divisores de zero em Zm.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/AA-26.pdf\" target=\"_blank\" rel=\"noopener\">Aula 26<\/a>\u00a0 (21\/03\/25) &#8211; Elementos invers\u00edveis em Zm. Propriedades. Resolu\u00e7\u00e3o de exerc\u00edcios da lista 08.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/aa27.pdf\" target=\"_blank\" rel=\"noopener\">Aula 27<\/a> (23\/03\/25) &#8211; Resolu\u00e7\u00e3o de exerc\u00edcios da lista 06 [estudo ass\u00edncrono]<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/aa28.pdf\" target=\"_blank\" rel=\"noopener\">Aula 28<\/a>\u00a0(25\/03\/25) &#8211; Resolu\u00e7\u00e3o de exerc\u00edcios da lista 05 [estudo ass\u00edncrono].<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2025\/03\/Aa29.pdf\" target=\"_blank\" rel=\"noopener\">Aula 29<\/a> (26\/03\/25) &#8211; Resolu\u00e7\u00e3o de exerc\u00edcios da Lista 07.<\/p>\n<p>Aula 30 (28\/03\/25) &#8211; Aplica\u00e7\u00e3o da Prova 02.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][<\/p>\n<p style=\"text-align: center;\"><strong>Primeiro Semestre<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>C\u00e1lculo 3 (Turma T4)<\/strong><\/p>\n<p>Dando sequ\u00eancia aos estudos de C\u00e1lculo, nesta disciplina estudaremos o C\u00e1lculo diferencial e integral de fun\u00e7\u00f5es a v\u00e1rias vari\u00e1veis reais.<\/p>\n<p><strong>\u00a0Local<\/strong>: Pr\u00e9dio 05, sala 217. Segundas, quartas e sextas, a partir das 10h.<\/p>\n<p style=\"text-align: center;\"><strong>Plano de Ensino<\/strong><\/p>\n<p style=\"text-align: center;\">O Plano de ensino pode se baixado clicando <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/Zahn_C3_11100060_T4.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Datas das Provas<\/strong><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/Prv_01.pdf\" target=\"_blank\" rel=\"noopener\">Prova 01<\/a>: dia 24\/06\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/Prv_01-Gabarito-.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito <\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/Prv_02.pdf\" target=\"_blank\" rel=\"noopener\">Prova 02<\/a>: dia 26\/07\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/Ga2c3.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito <\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/Prv_03.pdf\" target=\"_blank\" rel=\"noopener\">Prova 03<\/a>: dia 30\/08\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2023\/04\/Gabp3c3.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/p>\n<p style=\"text-align: center;\">Exame: dia 04\/09\/24<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Listas de Exerc\u00edcios<\/strong><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/L1_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 01<\/a> &#8211; No\u00e7\u00f5es de Topologia.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/L2_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 02<\/a> &#8211; Fun\u00e7\u00f5es de v\u00e1rias vari\u00e1veis reais.\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/RespL2-c3.pdf\" target=\"_blank\" rel=\"noopener\">Resolu\u00e7\u00f5es <\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/L3_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 03<\/a> &#8211; Limites e continuidade a v\u00e1rias vari\u00e1veis.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/L4_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 04<\/a> &#8211; Derivadas de fun\u00e7\u00f5es vetoriais de uma vari\u00e1vel real. Derivadas parciais.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/L5_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 05<\/a> &#8211; Diferenciais. Regra da Cadeia. Vetor Gradiente<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/L6_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 06<\/a> &#8211; Propriedades do gradiente. Planos tangentes. Extremos relativos e absolutos.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/L7_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 07<\/a> &#8211; F\u00f3rmula de Taylor. Integrais definidas de fun\u00e7\u00f5es a v\u00e1rias vari\u00e1veis(primeiros conceitos)<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/L8_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 08<\/a> &#8211; Integrais duplas em regi\u00f5es retangulares e em regi\u00f5es mais gerais.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/L9_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 09<\/a> &#8211; Integrais duplas: coordenadas polares, mudan\u00e7a geral de coordenadas, integrais impr\u00f3prias.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/L10_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 10<\/a> -Integrais triplas.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/L11_c3.pdf\" target=\"_blank\" rel=\"noopener\">Lista 11<\/a> &#8211; Integrais de linha. Teoremas de Green, Gauss e Stokes.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Arquivos pdf das aulas<\/strong>: ser\u00e3o postados abaixo, \u00e0 medida em que a disciplina evolui no semestre.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C3a1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 01<\/a>\u00a0 (15\/04\/24) Apresenta\u00e7\u00e3o da disciplina. Espa\u00e7os m\u00e9tricos. Bolas abertas e fechadas em um espa\u00e7o m\u00e9trico.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C3a2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 02<\/a> (17\/04\/24) Interior de um conjunto. Conjuntos abertos. Sequ\u00eancias em um espa\u00e7o m\u00e9trico. Ponto aderente de um conjunto. Fecho e conjunto fechado. Fronteira de um conjunto. Ponto de acumula\u00e7\u00e3o. Conjunto compacto.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C3a3.pdf\" target=\"_blank\" rel=\"noopener\">Aula 03<\/a> (19\/04\/24) Introdu\u00e7\u00e3o \u00e0s fun\u00e7\u00f5es de v\u00e1rias vari\u00e1veis reais de Rm em Rn. Fun\u00e7\u00f5es vetoriais. Exemplos de gr\u00e1ficos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C3a4.pdf\" target=\"_blank\" rel=\"noopener\">Aula 04<\/a>\u00a0 (22\/04\/24) Limites e derivadas de fun\u00e7\u00f5es vetoriais. Dom\u00ednio de fun\u00e7\u00f5es escales de R2 em R.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C3a5.pdf\" target=\"_blank\" rel=\"noopener\">Aula 05<\/a>\u00a0 \u00a0(24\/04\/24) Gr\u00e1ficos de fun\u00e7\u00f5es de R2 em R.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C3a6.pdf\" target=\"_blank\" rel=\"noopener\">Aula 06<\/a>\u00a0 (26\/04\/24) Limites de fun\u00e7\u00f5es de Rm em Rn.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C3a7.pdf\" target=\"_blank\" rel=\"noopener\">Aula 07<\/a>\u00a0 (29\/04\/24) Limites por caminhos. O teorema do Sandu\u00edche.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/05\/c3a8.pdf\" target=\"_blank\" rel=\"noopener\">Aula 08<\/a>\u00a0 (03\/05\/24) Continuidade em Rm. Teorema de Weierstrass.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/05\/C3-a-9.pdf\" target=\"_blank\" rel=\"noopener\">Aula 09<\/a> (06\/05\/24) Aula de exerc\u00edcios, sobre a lista 01.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C3-a10.pdf\" target=\"_blank\" rel=\"noopener\">Aula 10<\/a>\u00a0 (10\/06\/24) Revis\u00e3o de conte\u00fados de v\u00e1rias aulas [retomada das atividades ap\u00f3s suspens\u00e3o das aulas devido aos alagamentos no RS].<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C3a11.pdf\" target=\"_blank\" rel=\"noopener\">Aula 11<\/a>\u00a0 (12\/06\/24) Uma revis\u00e3o sobre continuidade e sobre derivadas de fun\u00e7\u00f5es vetoriais de uma vari\u00e1vel real. Derivadas parciais. Conceito e exemplos. Significado geom\u00e9trico da derivada parcial.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C3a12.pdf\" target=\"_blank\" rel=\"noopener\">Aula 12<\/a>\u00a0(14\/06\/24) Derivadas de ordem mais alta. Teorema de Schwarz.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C3a13.pdf\" target=\"_blank\" rel=\"noopener\">Aula13<\/a>\u00a0 (17\/06\/24) Diferenciabilidade no Rm. A matriz Jacobiana.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C3a14.pdf\" target=\"_blank\" rel=\"noopener\">Aula 14<\/a> (19\/06\/24) Diferenciabilidade, parte 2. Resolu\u00e7\u00e3o de exerc\u00edcios da lista 01.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C3a15.pdf\" target=\"_blank\" rel=\"noopener\">Aula 15<\/a>\u00a0(21\/06\/24) Aula de exerc\u00edcios, sobre a Lista 03.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C3a16.pdf\" target=\"_blank\" rel=\"noopener\">Aula 16<\/a> (22\/06\/24) Aula extra de exerc\u00edcios, sobre as listas 03 e 04, gravado no eaula.<\/p>\n<p>Aula 17 (24\/06\/24) Realiza\u00e7\u00e3o da Prova 01.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/Caderno-sem-titulo-37.pdf\" target=\"_blank\" rel=\"noopener\">Aula 18<\/a>\u00a0(26\/06\/24) Incrementos. Conceito de diferenciabilidade via incrementos. O diferencial total. Teorema da regra da cadeia, parte 1.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/c3a19.pdf\" target=\"_blank\" rel=\"noopener\">Aula 19<\/a> (28\/06\/24) Regra da Cadeia, parte 2.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a20.pdf\" target=\"_blank\" rel=\"noopener\">Aula 20<\/a> (01\/07\/24) Derivada direcional e o vetor gradiente.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a21.pdf\" target=\"_blank\" rel=\"noopener\">Aula 21<\/a>\u00a0(03\/07\/24) Plano tangente a uma superf\u00edcie. Extremos relativos e absolutos de fun\u00e7\u00f5es escalares a v\u00e1rias vari\u00e1veis.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a22.pdf\" target=\"_blank\" rel=\"noopener\">Aula 22<\/a> (05\/07\/24) Pontos cr\u00edticos. Classifica\u00e7\u00e3o de extremos relativos pelo teste da derivada parcial segundo, via matriz Hessiana.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a23.pdf\" target=\"_blank\" rel=\"noopener\">Aula 23<\/a>\u00a0(08\/07\/24) Mais um resultado envolvendo m\u00e1ximos e m\u00ednimos. F\u00f3rmula de Taylor com resto na forma de Lagrange, para fun\u00e7\u00f5es de R2 em R.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a24.pdf\" target=\"_blank\" rel=\"noopener\">Aula 24<\/a> (10\/07\/24) Um exemplo de uso da f\u00f3rmula de Taylor.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a25.pdf\" target=\"_blank\" rel=\"noopener\">Aula 25<\/a> (12\/07\/24) Blocos em Rm. Parti\u00e7\u00e3o de um bloco. Refinamento. Somas superior e inferior de uma fun\u00e7\u00e3o limitada em um bloco.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a26.pdf\" target=\"_blank\" rel=\"noopener\">Aula 26<\/a>\u00a0(15\/07\/24) Integrais inferior e superior. A integral definida. Crit\u00e9rio de integrabilidade. Exemplos de c\u00e1lculo via somas de Riemann.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a27.pdf\" target=\"_blank\" rel=\"noopener\">Aula 27<\/a>\u00a0 (17\/07\/24) Propriedades da integral definida em um bloco. Conjunto de medida nula. O Teorema de Lebesgue. A fun\u00e7\u00e3o caracter\u00edstica e conjuntos Jordan-mensur\u00e1veis. A integral definida em um conjunto Jordan-mensur\u00e1vel.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/c3\u304228.pdf\" target=\"_blank\" rel=\"noopener\">Aula 28<\/a>\u00a0(19\/07\/24) O Teorema de Lebesgue para conjuntos J mensur\u00e1veis. A integral de Riemann. Integrais duplas em regi\u00f5es retangulares.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a29.pdf\" target=\"_blank\" rel=\"noopener\">Aula 29<\/a>\u00a0(22\/07\/24) Integrais duplas em regi\u00f5es mais gerais.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a30.pdf\" target=\"_blank\" rel=\"noopener\">Aula 30<\/a>\u00a0(24\/07\/24) Aula de exerc\u00edcios. Resolu\u00e7\u00e3o de quest\u00f5es da lista 06.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a31.pdf\" target=\"_blank\" rel=\"noopener\">Aula 31<\/a>\u00a0 (25\/07\/24) Aula extra- Resolu\u00e7\u00e3o de exerc\u00edcios das listas.<\/p>\n<p>Aula 32 (26\/07\/24) Aplica\u00e7\u00e3o da Prova 02.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a33.pdf\" target=\"_blank\" rel=\"noopener\">Aula 33<\/a> (29\/07\/24) Outros exemplos de c\u00e1lculo de integrais duplas em regi\u00f5es mais gerais. Mudan\u00e7a de ordem de integra\u00e7\u00e3o. \u00c1rea de uma regi\u00e3o do plano. O teorema da m\u00e9dia.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C3a34.pdf\" target=\"_blank\" rel=\"noopener\">Aula 34<\/a> (31\/07\/24) Demonstra\u00e7\u00e3o do Teorema da m\u00e9dia. O sistema de coordenadas polares. Integrais duplas em coordenadas polares.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a35.pdf\" target=\"_blank\" rel=\"noopener\">Aula 35<\/a> (02\/08\/24) Exemplos de c\u00e1lculo de integrais duplas via coordenadas polares. Mudan\u00e7a geral de coordenadas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a36.pdf\" target=\"_blank\" rel=\"noopener\">Aula 36<\/a>\u00a0 (05\/08\/24) Exemplos de integrais usando mudan\u00e7a de coordenadas. Integrais impr\u00f3prias de primeiro e segundo tipo.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a37.pdf\" target=\"_blank\" rel=\"noopener\">Aula 37<\/a> (07\/08\/24) &#8211; Exemplos de integrais impr\u00f3prias. Integrais triplas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a38.pdf\" target=\"_blank\" rel=\"noopener\">Aula 38<\/a>\u00a0 (09\/08\/24) &#8211; Exemplos de c\u00e1lculo de volumes por integrais triplas. Mudan\u00e7a geral de vari\u00e1veis para integrais triplas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3A39.pdf\" target=\"_blank\" rel=\"noopener\">Aula 39<\/a> (12\/08\/24) -Exemplos de aplica\u00e7\u00e3o de c\u00e1lculo de mudan\u00e7a de coordenadas. Sistemas de coordenadas cil\u00edndricas e esf\u00e9ricas e o c\u00e1lculo de integrais triplas nesses sistemas.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3-a-40.pdf\" target=\"_blank\" rel=\"noopener\">Aula 40<\/a> (13\/08\/24) &#8211; Resolu\u00e7\u00e3o de exerc\u00edcios das listas 08 e 09 [aula extra, gravada no e-aula].<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a41.pdf\" target=\"_blank\" rel=\"noopener\">Aula 41<\/a>\u00a0 (14\/08\/24) &#8211; Um interessante exemplo de integrais triplas via coordenadas esf\u00e9ricas. Resolu\u00e7\u00e3o de exerc\u00edcios das listas 08 e 09.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a42.pdf\" target=\"_blank\" rel=\"noopener\">Aula 42<\/a>\u00a0 (16\/08\/24) &#8211; Campos vetoriais. Campos gradientes. Divergente de um campo vetorial.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a43.pdf\" target=\"_blank\" rel=\"noopener\">Aula 43<\/a>\u00a0 (19\/08\/24) &#8211; Rotacional de um campo vetorial. integral de linha.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3-a44.pdf\" target=\"_blank\" rel=\"noopener\">Aula 44<\/a> \u00a0(21\/08\/24) &#8211; Independ\u00eancia da parametriza\u00e7\u00e3o na integral de linha.curvas simples e n\u00e3o simples. Teorema Fundamental do C\u00e1lculo para Campos gradientes.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a45.pdf\" target=\"_blank\" rel=\"noopener\">Aula 45<\/a> (23\/08\/24) &#8211; Integral de linha em caminhos fechados. O teorema de Green.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a46.pdf\" target=\"_blank\" rel=\"noopener\">Aula 46<\/a> (26\/08\/24) &#8211; Exemplos de uso do Teorema de Green. Curva parametrizada pelo comprimento de arco. Vers\u00f5es vetoriais do Teorema de Green: teoremas da diverg\u00eancia e de Stokes.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a47.pdf\" target=\"_blank\" rel=\"noopener\">Aula 47<\/a>\u00a0(27\/08\/24) &#8211; Aula extra, de exerc\u00edcios.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C3a48.pdf\" target=\"_blank\" rel=\"noopener\">Aula 48<\/a>\u00a0(28\/08\/24) &#8211; Aula de exerc\u00edcios.<\/p>\n<p>Aula 49 (30\/08\/24) &#8211; Realiza\u00e7\u00e3o da Prova 03.<\/p>\n<p>Aula 50 (04\/09\/24) &#8211; Entrega das proas. Realiza\u00e7\u00e3o da Prova de recupera\u00e7\u00e3o.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p style=\"text-align: center;\"><strong>C\u00e1lculo 1 (Turma T1)<\/strong><\/p>\n<p>Nesta disciplina faremos uma revis\u00e3o de t\u00f3picos relevantes sobre conjuntos e \u00a0o estudo do corpo ordenado e completo dos n\u00fameros reais, al\u00e9m de um estudo de fun\u00e7\u00f5es (elementos, opera\u00e7\u00f5es, tipos de fun\u00e7\u00f5es, gr\u00e1ficos). Em seguida, focaremos nosso estudo na teoria de limites e continuidade. Por fim, apresentamos o importante estudo de derivadas e suas importantes aplica\u00e7\u00f5es.<\/p>\n<p><strong>Hor\u00e1rios:<\/strong> Ter\u00e7as e quintas, sala 429 &#8211; Campus Anglo, a partir das 8h.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Plano de ensino<\/strong><\/p>\n<p>Uma c\u00f3pia do arquivo pdf do plano de ensino pode ser baixado clicando <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/Zahn_c1_11100058_T1-3.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Datas das Provas<\/strong><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/PR_01_T1.pdf\" target=\"_blank\" rel=\"noopener\">Prova 01<\/a>: 18\/07\/24 &#8211; <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/Gabarito-P1T1.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/PR_02_T1.pdf\" target=\"_blank\" rel=\"noopener\">Prova 02<\/a>: 03\/09\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gabp2c1t1.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Prova_Optativa.pdf\" target=\"_blank\" rel=\"noopener\">Optativa<\/a>: 05\/09\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/GabOptc1.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/p>\n<p style=\"text-align: center;\">Exame: 10\/09\/24<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Listas de Exerc\u00edcios<\/strong><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/lista_01-1.pdf\" target=\"_blank\" rel=\"noopener\">Lista 01<\/a> &#8211; Conjuntos e fun\u00e7\u00f5es<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/lista_02.pdf\" target=\"_blank\" rel=\"noopener\">Lista 02<\/a> &#8211; No\u00e7\u00f5es de Trigonometria<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/lista_03.pdf\" target=\"_blank\" rel=\"noopener\">Lista 03<\/a> &#8211; Fun\u00e7\u00f5es trigonom\u00e9tricas diretas. Limites de fun\u00e7\u00f5es (primeiros conceitos)<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/lista_04.pdf\" target=\"_blank\" rel=\"noopener\">Lista 04<\/a> &#8211; Limites de fun\u00e7\u00f5es<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_05.pdf\" target=\"_blank\" rel=\"noopener\">Lista 05<\/a> &#8211; Fun\u00e7\u00f5es cont\u00ednuas.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_06.pdf\" target=\"_blank\" rel=\"noopener\">Lista 06<\/a> &#8211; Derivadas (primeiros conceitos)<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_07.pdf\" target=\"_blank\" rel=\"noopener\">Lista 07<\/a> &#8211; Regras de deriva\u00e7\u00e3o. Deriva\u00e7\u00e3o impl\u00edcita. Diferenciais<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_08.pdf\" target=\"_blank\" rel=\"noopener\">Lista 08<\/a> &#8211; Taxas relacionadas<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_09.pdf\" target=\"_blank\" rel=\"noopener\">Lista 09<\/a> &#8211; Problemas de m\u00e1ximos e m\u00ednimos<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Material de leitura e estudo extra, et cetera:<\/strong><\/p>\n<ul>\n<li>Texto <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/Crise-Rac.pdf\" target=\"_blank\" rel=\"noopener\">&#8220;A crise dos racionais&#8221;<\/a>, referente aos conte\u00fados trabalhados na Aula 02.<\/li>\n<li>Texto &#8220;<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/05\/Vos_digo.pdf\" target=\"_blank\" rel=\"noopener\">Em verdade vos digo&#8230;<\/a>&#8220;, referente ao estudo da fun\u00e7\u00e3o quadr\u00e1tica (aulas 05 e 06).<\/li>\n<li>Texto &#8220;<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/logs.pdf\" target=\"_blank\" rel=\"noopener\">Propriedades emoji-logar\u00edtmicas<\/a>&#8220;, referente ao estudo de logaritmos (aula 09).<\/li>\n<li>clique <a href=\"https:\/\/wp.ufpel.edu.br\/projetogama\/files\/2019\/06\/FORMULARIO_GAMA_2019_1.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a> para baixar um arquivo PDF do Formul\u00e1rio do Gama.<\/li>\n<li>Resolu\u00e7\u00e3o de quest\u00f5es da Lista 08 (taxas relacionadas), acesso\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2017\/03\/Resp_c1_L9.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Arquivos pdf das aulas<\/strong><\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/A1-.pdf\" target=\"_blank\" rel=\"noopener\">Aula 01<\/a>\u00a0(18\/04\/24) &#8211; Apresenta\u00e7\u00e3o da disciplina. Conjuntos. Rela\u00e7\u00f5es de pertin\u00eancia e conten\u00e7\u00e3o. O conjunto vazio. Opera\u00e7\u00f5es entre conjuntos e rela\u00e7\u00f5es com portas l\u00f3gicas. Propriedades dos conjuntos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C1-a2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 02<\/a>\u00a0(23\/04\/24) &#8211; O corpo dos racionais e sua insufici\u00eancia. O corpo ordenado e completo R dos n\u00fameros reais. Rela\u00e7\u00e3o de ordem e intervalos. Inequa\u00e7\u00f5es.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/c1-a-3.pdf\" target=\"_blank\" rel=\"noopener\">Aula 03<\/a> (25\/04\/24) &#8211; M\u00f3dulo e propriedades. Inequa\u00e7\u00f5es envolvendo m\u00f3dulos. Fun\u00e7\u00f5es de uma vari\u00e1vel real: primeiros conceitos. Igualdade de fun\u00e7\u00f5es. Fun\u00e7\u00f5es pares e \u00edmpares.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C1a4.pdf\" target=\"_blank\" rel=\"noopener\">Aula 04<\/a> (30\/04\/24) &#8211; Composi\u00e7\u00e3o de fun\u00e7\u00f5es. Injetividade, sobrejetividade e bijetividade.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/05\/c1a5.pdf\" target=\"_blank\" rel=\"noopener\">Aula 05<\/a>\u00a0 (02\/05\/24) &#8211; Fun\u00e7\u00f5es crescentes e decrescentes. Fun\u00e7\u00f5es afim e quadr\u00e1tica.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t1a6.pdf\" target=\"_blank\" rel=\"noopener\">Aula 06<\/a> (11\/06\/24) &#8211; Revis\u00e3o de conte\u00fados das aulas anteriores.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t1a7.pdf\" target=\"_blank\" rel=\"noopener\">Aula o7<\/a>\u00a0(13\/06\/24) &#8211; Continua\u00e7\u00e3o da revis\u00e3o. Fun\u00e7\u00e3o quadr\u00e1tica, parte II. Fun\u00e7\u00f5es modulares.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t1a8.pdf\" target=\"_blank\" rel=\"noopener\">Aula 08<\/a>\u00a0 (18\/06\/24) &#8211; Fun\u00e7\u00e3o exponencial.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1r1a9.pdf\" target=\"_blank\" rel=\"noopener\">Aula 09<\/a>\u00a0 (20\/06\/24) &#8211; Logaritmos. Fun\u00e7\u00e3o logar\u00edtmica.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t1a10.pdf\" target=\"_blank\" rel=\"noopener\">Aula 10<\/a>\u00a0 (25\/06\/24) &#8211; Um exerc\u00edcio envolvendo exponenciais e logaritmos. Trigonometria no tri\u00e2ngulo ret\u00e2ngulo. Arcos not\u00e1veis. Ciclo trigonom\u00e9trico. Express\u00e3o geral dos arcos e menor indetermina\u00e7\u00e3o. Rela\u00e7\u00e3o entre grau e radiano.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t1a11.pdf\" target=\"_blank\" rel=\"noopener\">Aula 11<\/a>\u00a0(27\/06\/24) &#8211; N\u00fameros trigonom\u00e9tricos no ciclo. Simetrias e redu\u00e7\u00e3o ao primeiro quadrante.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/c1t1a12.pdf\" target=\"_blank\" rel=\"noopener\">Aula 12<\/a> (29\/06\/24) &#8211; F\u00f3rmulas de adi\u00e7\u00e3o e subtra\u00e7\u00e3o de arcos. Arcos duplos e arcos metade [estudo remoto].<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a13.pdf\" target=\"_blank\" rel=\"noopener\">Aula 13<\/a> (02\/07\/24) &#8211; Fun\u00e7\u00f5es trigonom\u00e9tricas diretas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a14.pdf\" target=\"_blank\" rel=\"noopener\">Aula 14<\/a>\u00a0(04\/07\/24) &#8211; Ponto de acumula\u00e7\u00e3o de um conjunto. Limites de fun\u00e7\u00f5es de uma vari\u00e1vel real: defini\u00e7\u00e3o formal. Exemplos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a15.pdf\" target=\"_blank\" rel=\"noopener\">Aula 15<\/a>\u00a0 (09\/07\/24) &#8211; Outros exemplos de limites pela defini\u00e7\u00e3o. Propriedades aritm\u00e9ticas dos limites.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a16.pdf\" target=\"_blank\" rel=\"noopener\">Aula 16<\/a>\u00a0 (11\/07\/24) &#8211; Teorema do sandu\u00edche. Limites infinitos e no infinito. Indetermina\u00e7\u00e3o do tipo 0\/0.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a17.pdf\" target=\"_blank\" rel=\"noopener\">Aula 17<\/a>\u00a0 (13\/07\/24) &#8211; Aula de exerc\u00edcios, sobre a Lista 02 [ gravada no e-aula]<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a18.pdf\" target=\"_blank\" rel=\"noopener\">Aula 18<\/a>\u00a0 (16\/07\/24) &#8211; Aula de exerc\u00edcios.<\/p>\n<p>Aula 19 (18\/07\/24) &#8211; Aplica\u00e7\u00e3o da Prova 01.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a20.pdf\" target=\"_blank\" rel=\"noopener\">Aula 20<\/a> (23\/07\/24) &#8211; Limites laterais. Limites infinitos. Limites no infinito. Esbo\u00e7os gr\u00e1ficos com ajuda de limites laterais, infinitos e no infinito.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a21.pdf\" target=\"_blank\" rel=\"noopener\">Aula 21<\/a> \u00a0(25\/07\/24) &#8211; Mais um exemplo de esbo\u00e7o gr\u00e1fico via limites laterais, infinitos e no infinito. O Limite trigonom\u00e9trico fundamental.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a22.pdf\" target=\"_blank\" rel=\"noopener\">Aula 22<\/a> \u00a0(30\/07\/24) &#8211; Exemplos envolvendo o limite trigonom\u00e9trico fundamental. O limite exponencial fundamental.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a23.pdf\" target=\"_blank\" rel=\"noopener\">Aula 23<\/a> (01\/08\/24) &#8211; Fun\u00e7\u00f5es cont\u00ednuas. Fun\u00e7\u00f5es cont\u00ednuas em intervalos: teoremas de Weierstrass e do valor intermedi\u00e1rio.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a24.pdf\" target=\"_blank\" rel=\"noopener\">Aula 24<\/a>\u00a0 (06\/08\/24) &#8211; Fun\u00e7\u00f5es descont\u00ednuas. Derivadas: defini\u00e7\u00e3o. C\u00e1lculo de derivadas pela defini\u00e7\u00e3o. Significado geom\u00e9trico da derivada.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a25.pdf\" target=\"_blank\" rel=\"noopener\">Aula 25<\/a>\u00a0 (08\/08\/24) &#8211; Significado f\u00edsico da derivada. Derivadas laterais. Primeiras regras de deriva\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a26.pdf\" target=\"_blank\" rel=\"noopener\">Aula 26<\/a>\u00a0 (13\/08\/24) &#8211; Regras de deriva\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a27.pdf\" target=\"_blank\" rel=\"noopener\">Aula 27<\/a>\u00a0 (15\/08\/24) &#8211; Derivada como aproxima\u00e7\u00e3o linear. Diferenciais. Regra da cadeia. Deriva\u00e7\u00e3o impl\u00edcita.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a28.pdf\" target=\"_blank\" rel=\"noopener\">Aula 28<\/a>\u00a0(20\/08\/24) &#8211; Taxas relacionadas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a29.pdf\" target=\"_blank\" rel=\"noopener\">Aula 29<\/a> (21\/08\/24) &#8211; Aula extra, pelo eaula &#8211; Derivadas das fun\u00e7\u00f5es trigonom\u00e9tricas inversas. Resolu\u00e7\u00e3o de exerc\u00edcios das Listas 04, 05 e 06.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a30.pdf\" target=\"_blank\" rel=\"noopener\">Aula 30<\/a>\u00a0 \u00a0(22\/08\/24) &#8211; Derivadas de ordem superior. Extremos relativos, \u00a0concavidade e ponto de inflex\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a31.pdf\" target=\"_blank\" rel=\"noopener\">Aula 31<\/a> (27\/08\/24) &#8211; Aula de exerc\u00edcios, da lista 09.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t1a32.pdf\" target=\"_blank\" rel=\"noopener\">Aula 32<\/a>\u00a0 (29\/08\/24) &#8211; Aula de exerc\u00edcios.<\/p>\n<p>Aula 33 (03\/09\/24) &#8211; Realiza\u00e7\u00e3o da segunda Prova.<\/p>\n<p>Aula 34 (05\/09\/24) &#8211; Realiza\u00e7\u00e3o da Prova Optativa.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;&lt;&gt;<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>C\u00e1lculo 1 (Turma T2)<\/strong><\/p>\n<p>Nesta disciplina faremos uma revis\u00e3o de t\u00f3picos relevantes sobre conjuntos e \u00a0o estudo do corpo ordenado e completo dos n\u00fameros reais, al\u00e9m de um estudo de fun\u00e7\u00f5es (elementos, opera\u00e7\u00f5es, tipos de fun\u00e7\u00f5es, gr\u00e1ficos). Em seguida, focaremos nosso estudo na teoria de limites e continuidade. Por fim, apresentamos o importante estudo de derivadas e suas importantes aplica\u00e7\u00f5es.<\/p>\n<p><strong>Hor\u00e1rios:<\/strong> Ter\u00e7as e quintas, sala 429 &#8211; Campus Anglo, a partir das 10h.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Plano de ensino<\/strong><\/p>\n<p style=\"text-align: center;\">Uma c\u00f3pia do arquivo pdf pode ser acessada clicando <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/Zahn_c1_11100058_T2.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/p>\n<p style=\"text-align: center;\"><strong>Listas de exerc\u00edcios\u00a0<\/strong><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/lista_01-1.pdf\" target=\"_blank\" rel=\"noopener\">Lista 01<\/a> &#8211; Conjuntos e fun\u00e7\u00f5es<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/lista_02_T2.pdf\" target=\"_blank\" rel=\"noopener\">Lista 02<\/a> &#8211; No\u00e7\u00f5es sobre Trigonometria<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/lista_03T_2.pdf\" target=\"_blank\" rel=\"noopener\">Lista 03<\/a> &#8211; Fun\u00e7\u00f5es trigonom\u00e9tricas &#8211; Estudo de limites<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/lista_04.pdf\" target=\"_blank\" rel=\"noopener\">Lista 04<\/a> &#8211; Limites de fun\u00e7\u00f5es<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_05.pdf\" target=\"_blank\" rel=\"noopener\">Lista 05<\/a> &#8211; Fun\u00e7\u00f5es cont\u00ednuas.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_06.pdf\" target=\"_blank\" rel=\"noopener\">Lista 06<\/a> &#8211; Derivadas (primeiros conceitos)<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_07.pdf\" target=\"_blank\" rel=\"noopener\">Lista 07<\/a> &#8211; Regras de deriva\u00e7\u00e3o. Deriva\u00e7\u00e3o impl\u00edcita. Diferenciais<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_08.pdf\" target=\"_blank\" rel=\"noopener\">Lista 08<\/a> &#8211; Taxas relacionadas<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/lista_09.pdf\" target=\"_blank\" rel=\"noopener\">Lista 09<\/a> &#8211; Problemas de m\u00e1ximos e m\u00ednimos<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Datas das Provas<\/strong><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/PR_01_T2.pdf\" target=\"_blank\" rel=\"noopener\">Prova 01<\/a>: 18\/07\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/Gabarito-P1T2.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/PR_02_T2.pdf\" target=\"_blank\" rel=\"noopener\">Prova 02<\/a>: 03\/09\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Gabp2c1t2.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/Prova_Optativa.pdf\" target=\"_blank\" rel=\"noopener\">Optativa<\/a>: 05\/09\/24 &#8211;\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/09\/GabOptc1.pdf\" target=\"_blank\" rel=\"noopener\">Gabarito<\/a><\/p>\n<p style=\"text-align: center;\">Exame: 10\/09\/24<\/p>\n<p style=\"text-align: center;\"><strong>Material de leitura e estudo extra, et cetera:<\/strong><\/p>\n<ul>\n<li>Texto <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/Crise-Rac.pdf\" target=\"_blank\" rel=\"noopener\">&#8220;A crise dos racionais&#8221;<\/a>, referente aos conte\u00fados trabalhados na Aula 02.<\/li>\n<li>clique <a href=\"https:\/\/wp.ufpel.edu.br\/projetogama\/files\/2019\/06\/FORMULARIO_GAMA_2019_1.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a> para baixar um arquivo PDF do Formul\u00e1rio do Gama.<\/li>\n<li>Resolu\u00e7\u00e3o de quest\u00f5es da Lista 08 (taxas relacionadas), acesso\u00a0<a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2017\/03\/Resp_c1_L9.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Arquivos pdf das aulas<\/strong><\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t2a1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 01<\/a>\u00a0 (11\/06\/24) &#8211; Apresenta\u00e7\u00e3o da disciplina. Conjuntos e opera\u00e7\u00f5es<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t2a2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 02<\/a>\u00a0 (13\/06\/24) &#8211; Os racionais com um corpo ordenado e sua insuficiencia. O corpo ordenado dos n\u00fameros reais. Intervalos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t2a3.pdf\" target=\"_blank\" rel=\"noopener\">Aula 03<\/a> (18\/06\/24) &#8211; Inequa\u00e7\u00f5es em R. M\u00f3dulo de um n\u00famero real e propriedades.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t2a4.pdf\" target=\"_blank\" rel=\"noopener\">Aula 04<\/a>\u00a0(20\/06\/24) &#8211; Inequa\u00e7\u00f5es envolvendo m\u00f3dulo. Estudo de fun\u00e7\u00f5es. Conceitos. Dom\u00ednio a partir da lei.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t2a5.pdf\" target=\"_blank\" rel=\"noopener\">Aula 05<\/a>\u00a0 (25\/06\/24) &#8211; Paridade de fun\u00e7\u00f5es. Opera\u00e7\u00f5es com fun\u00e7\u00f5es. Composi\u00e7\u00e3o de fun\u00e7\u00f5es. Injetividade, sobrejetividade e bijetividade.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t2a6.pdf\" target=\"_blank\" rel=\"noopener\">Aula 06<\/a> (27\/06\/24) &#8211; Mais sobre composi\u00e7\u00f5es. Fun\u00e7\u00e3o afim. Fun\u00e7\u00e3o quadr\u00e1tica, parte 1.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a7.pdf\" target=\"_blank\" rel=\"noopener\">Aula 07<\/a>\u00a0 (02\/07\/24) &#8211; Fun\u00e7\u00e3o quadr\u00e1tica, parte 2. Fun\u00e7\u00e3o modular.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a8.pdf\" target=\"_blank\" rel=\"noopener\">Aula 08<\/a>\u00a0 (04\/07\/24) &#8211; Fun\u00e7\u00e3o exponencial. Logaritmos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a9.pdf\" target=\"_blank\" rel=\"noopener\">Aula 09<\/a>\u00a0(09\/07\/24) &#8211; Fun\u00e7\u00e3o logar\u00edtmica. Limites de fun\u00e7\u00f5es de uma vari\u00e1vel real: defini\u00e7\u00e3o formal e exemplos.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a10.pdf\" target=\"_blank\" rel=\"noopener\">Aula 10<\/a>\u00a0 (11\/07\/24) &#8211; Outros exemplos de limites pela defini\u00e7\u00e3o. Propriedades aritm\u00e9ticas. Indetermina\u00e7\u00e3o do tipo 0\/0.<\/p>\n<p>Aulas <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t1a10.pdf\" target=\"_blank\" rel=\"noopener\">11<\/a>, <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/06\/C1t1a11.pdf\" target=\"_blank\" rel=\"noopener\">12<\/a> e <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t1a13.pdf\" target=\"_blank\" rel=\"noopener\">13<\/a> &#8211; Estudo individual da trigonometria e fun\u00e7\u00f5es trigonom\u00e9tricas diretas [aulas dadas na turma T1]<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a14.pdf\" target=\"_blank\" rel=\"noopener\">Aula 14<\/a>\u00a0 (13\/07\/24) &#8211; Aula de exerc\u00edcios, sobre a lista 03 [ gravada no e-aula]<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a15.pdf\" target=\"_blank\" rel=\"noopener\">Aula 15<\/a> (16\/07\/24) &#8211; Aula de exerc\u00edcios.<\/p>\n<p>Aula 16 (18\/07\/24) &#8211; Aplica\u00e7\u00e3o da Prova 01.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a17.pdf\" target=\"_blank\" rel=\"noopener\">Aula 17<\/a>\u00a0 (23\/07\/24) &#8211; limites no infinito Indetermina\u00e7\u00e3o da forma infinito\/infinito. Limites laterais. Gr\u00e1ficos de fun\u00e7\u00f5es com aux\u00edlio de limites laterais e no infinito.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a18.pdf\" target=\"_blank\" rel=\"noopener\">Aula 18<\/a>\u00a0 (25\/07\/24) &#8211; Mais exemplos de esbo\u00e7os gr\u00e1ficos de fun\u00e7\u00f5es racionais via limites infinitos, laterais e no infinito. Limite trigonom\u00e9trico fundamental.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/07\/C1t2a19.pdf\" target=\"_blank\" rel=\"noopener\">Aula 19<\/a> (30\/07\/24) &#8211; Exemplos envolvendo o limite trigonom\u00e9trico fundamental. O limite exponencial fundamental.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 20<\/a> (01\/08\/24) &#8211; Fun\u00e7\u00f5es cont\u00ednuas. Fun\u00e7\u00f5es cont\u00ednuas em intervalos: teoremas de Weierstrass e do valor intermedi\u00e1rio.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2a21.pdf\" target=\"_blank\" rel=\"noopener\">Aula 21<\/a> (06\/08\/24) &#8211; Fun\u00e7\u00f5es descont\u00ednuas. Derivadas: defini\u00e7\u00e3o. C\u00e1lculo de derivadas pela defini\u00e7\u00e3o. Significado geom\u00e9trico da derivada.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2a22.pdf\" target=\"_blank\" rel=\"noopener\">Aula 22<\/a>\u00a0 (08\/08\/22) &#8211; Significado f\u00edsico da derivada. Derivadas laterais. Primeiras regras de deriva\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2a23.pdf\" target=\"_blank\" rel=\"noopener\">Aula 23<\/a>\u00a0 (13\/08\/24) &#8211; Regras de deriva\u00e7\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2a24.pdf\" target=\"_blank\" rel=\"noopener\">Aula 24<\/a>\u00a0(15\/08\/24) &#8211; Derivada como aproxima\u00e7\u00e3o linear. Diferenciais. Regra da cadeia. Deriva\u00e7\u00e3o impl\u00edcita.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2023\/04\/C1t2a25.pdf\" target=\"_blank\" rel=\"noopener\">Aula 25<\/a> (17\/08\/24) &#8211; Aula extra, pelo e-aula &#8211; \u00a0Fun\u00e7\u00f5es inversas. derivadas das fun\u00e7\u00f5es trigonom\u00e9tricas inversas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2a26.pdf\" target=\"_blank\" rel=\"noopener\">Aula 26<\/a> (20\/08\/24) &#8211; Taxas relacionadas.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2-a-27.pdf\" target=\"_blank\" rel=\"noopener\">Aula 27<\/a>\u00a0 \u00a0(22\/08\/24) &#8211; Derivadas de ordem superior. Extremos relativos, \u00a0concavidade e ponto de inflex\u00e3o.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2a28.pdf\" target=\"_blank\" rel=\"noopener\">Aula 28<\/a> (27\/08\/24) &#8211; Aula de exerc\u00edcios sobre m\u00e1ximos e m\u00ednimos, sobre a lista 09.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/C1t2a30.pdf\" target=\"_blank\" rel=\"noopener\">Aula 30<\/a>\u00a0 (29\/08\/24) &#8211; Aula de exerc\u00edcios.<\/p>\n<p>Aula 31 (03\/09\/24) -Realiza\u00e7\u00e3o da segunda Prova.<\/p>\n<p>Aula 32 (05\/09\/24) &#8211; Realiza\u00e7\u00e3o da Prova Optativa.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">************************ \u00a0DISCILPINAS CANCELADAS ************************<\/p>\n<p style=\"text-align: center;\"><strong>C\u00e1lculo I (Matem\u00e1tica, Turma T2)<\/strong><\/p>\n<p style=\"text-align: center;\"><em><strong>ESTA DISCIPLINA FOI CANCELADA NA TERCEIRA SEMANA DE AULA POIS HAVIAM SOMENTE 3 ALUNOS MATRICULADOS.<\/strong><\/em><\/p>\n<p><em>Nesta disciplina estudaremos o C\u00e1lculo Diferencial a uma vari\u00e1vel real. Mais precisamente, estudaremos limites, continuidade e diferenciabilidade, bem como suas aplica\u00e7\u00f5es.<\/em><\/p>\n<p><em><strong>Local<\/strong>: Pr\u00e9dio 05, sala 217. Segundas, quartas e sextas, a partir das 8h.<\/em><\/p>\n<p style=\"text-align: center;\"><em><strong>Plano de Ensino<\/strong><\/em><\/p>\n<p style=\"text-align: center;\"><em>O Plano de ensino pode se baixado clicando <a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/CI_plano_ensino_2024_1_11100080_T2.pdf\" target=\"_blank\" rel=\"noopener\">aqui<\/a>.<\/em><\/p>\n<p style=\"text-align: center;\"><em><strong>Datas das Provas<\/strong><\/em><\/p>\n<p style=\"text-align: center;\"><em>Prova 01: dia 17\/05\/24 \u00a0Prova 02: dia 21\/06\/24.\u00a0Prova 03: dia 26\/07\/24.\u00a0Exame: dia 31\/07\/24<\/em><\/p>\n<p style=\"text-align: center;\"><em><strong>Listas de Exerc\u00edcios<\/strong><\/em><\/p>\n<p style=\"text-align: center;\"><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/lista_01.pdf\" target=\"_blank\" rel=\"noopener\">Lista 01<\/a> &#8211; Composi\u00e7\u00e3o de fun\u00e7\u00f5es, inventividade, sobrejetividade, bijetividade. Fun\u00e7\u00f5es inversas.<\/em><\/p>\n<p style=\"text-align: center;\"><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/lista_02.pdf\" target=\"_blank\" rel=\"noopener\">Lista 02<\/a> &#8211; Fun\u00e7\u00f5es hiperb\u00f3licas. Limites de fun\u00e7\u00f5es.<\/em><\/p>\n<p style=\"text-align: center;\"><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/lista_03.pdf\" target=\"_blank\" rel=\"noopener\">Lista 03<\/a> &#8211; Limites<\/em><\/p>\n<p><em><strong>Arquivos pdf das aulas<\/strong>: ser\u00e3o postados abaixo, \u00e0 medida em que a disciplina evolui no semestre.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C1-a-1.pdf\" target=\"_blank\" rel=\"noopener\">Aula 01<\/a>\u00a0 (15\/04\/24) Apresenta\u00e7\u00e3o do curso. Composi\u00e7\u00e3o de fun\u00e7\u00f5es. Fun\u00e7\u00f5es injetiva sobrejetiva e bijetiva. Propriedades envolvendo estes conceitos.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C1a2.pdf\" target=\"_blank\" rel=\"noopener\">Aula 02<\/a>\u00a0 (17\/04\/24) Fun\u00e7\u00f5es invers\u00edveis. Fun\u00e7\u00f5es hiperb\u00f3licas.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/Ci-a3.pdf\" target=\"_blank\" rel=\"noopener\">Aula 03<\/a>\u00a0(19\/04\/24) Demais fun\u00e7\u00f5es hiperb\u00f3licas diretas e propriedades.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C1-a4.pdf\" target=\"_blank\" rel=\"noopener\">Aula 04<\/a>\u00a0(22\/04\/23) Fun\u00e7\u00f5es hiperb\u00f3licas inversas.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/Ci-a5.pdf\" target=\"_blank\" rel=\"noopener\">Aula 05<\/a>\u00a0 (24\/04\/24) Algumas no\u00e7\u00f5es de Topologia. Limite de fun\u00e7\u00f5es: defini\u00e7\u00e3o e exemplos.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/C1a6.pdf\" target=\"_blank\" rel=\"noopener\">Aula 06<\/a>\u00a0 (26\/04\/24) Outros exemplos de c\u00e1lculo de limites por defini\u00e7\u00e3o. Unicidade do limite.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/04\/Cia7.pdf\" target=\"_blank\" rel=\"noopener\">Aula 07<\/a>\u00a0 (29\/04\/24) Propriedades aritm\u00e9ticas dos limites. Indetermina\u00e7\u00e3o da forma 0\/0.<\/em><\/p>\n<p><em><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/05\/C1a8.pdf\" target=\"_blank\" rel=\"noopener\">Aula 08<\/a> (03\/05\/24) Limites laterais. Limites infinitos.<\/em><\/p>\n<p style=\"text-align: center;\"><em>************************************************<\/em><\/p>\n<p style=\"text-align: center;\"><strong>Aulas de C\u00e1lculo I para o Prof Andrei:<\/strong><\/p>\n<p>\u00a0Aulas que ministrei para o professor Andrei, para a turma de Matem\u00e1tica do noturno: Estudos de an\u00e1lise gr\u00e1fica (estudo completo) de fun\u00e7\u00f5es. Marcaremos uma aula na sexta dia 09\/08, pelo Google Meet, a partir das 20:40.<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/A1.pdf\" target=\"_blank\" rel=\"noopener\">Aula A<\/a> (dia 07\/08\/24)<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/Aula-B.pdf\" target=\"_blank\" rel=\"noopener\">Aula B<\/a>\u00a0(dia 09\/08\/24)<\/p>\n<p><a href=\"https:\/\/wp.ufpel.edu.br\/zahn\/files\/2024\/08\/Aula-C.pdf\" target=\"_blank\" rel=\"noopener\">Aula C<\/a>\u00a0(dia 14\/08\/24)<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ano de 2024 de Nosso Senhor<\/p>\n","protected":false},"author":605,"featured_media":0,"parent":15,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-3815","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P7fXYa-Zx","_links":{"self":[{"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/pages\/3815","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/users\/605"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/comments?post=3815"}],"version-history":[{"count":2,"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/pages\/3815\/revisions"}],"predecessor-version":[{"id":3818,"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/pages\/3815\/revisions\/3818"}],"up":[{"embeddable":true,"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/pages\/15"}],"wp:attachment":[{"href":"https:\/\/wp.ufpel.edu.br\/zahn\/wp-json\/wp\/v2\/media?parent=3815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}