{"id":1945,"date":"2021-08-09T12:25:25","date_gmt":"2021-08-09T12:25:25","guid":{"rendered":"http:\/\/www.ime.unicamp.br\/~ddnovaes\/?p=1945"},"modified":"2023-06-26T16:46:00","modified_gmt":"2023-06-26T16:46:00","slug":"modelagem-matematica-e-equacoes-diferenciais","status":"publish","type":"post","link":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/2021\/08\/09\/modelagem-matematica-e-equacoes-diferenciais\/","title":{"rendered":"Modelagem Matem\u00e1tica e Equa\u00e7\u00f5es Diferenciais"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\"><strong>MA 312&nbsp;&#8211; Turma&nbsp;<\/strong>Z<\/h3>\n\n\n\n<p><strong>Link Permanente do Meet:<\/strong><a rel=\"noreferrer noopener\" href=\"https:\/\/meet.google.com\/bvg-bffg-kny\" target=\"_blank\"> <\/a><a rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\" target=\"_blank\" href=\"http:\/\/meet.google.com\/peb-dbji-wym\">meet.google.com\/peb-dbji-wym<\/a><\/p>\n\n\n\n<p><em>O acesso a sala \u00e9 garantido somente se logado \u00e0 conta institucional da UNICAMP.<\/em><\/p>\n\n\n\n<p><strong>Ementa:<\/strong> Equa\u00e7\u00f5es diferenciais de 1\u00aa ordem: equa\u00e7\u00f5es separ\u00e1veis, modelos b\u00e1sicos: din\u00e2mica de popula\u00e7\u00f5es, estabilidade, resfriamento de um corpo. Equa\u00e7\u00f5es diferenciais de 2\u00aa ordem, modelos b\u00e1sicos; din\u00e2mica de uma part\u00edcula, oscilador harm\u00f4nico, campos centrais de for\u00e7as. Transformada de Laplace. Teoria b\u00e1sica de sistemas de equa\u00e7\u00f5es diferenciais: equa\u00e7\u00f5es alg\u00e9bricas, autovalores, autovetores; sistemas lineares homog\u00eaneos com coeficientes constantes; sistemas lineares n\u00e3o homog\u00eaneos; varia\u00e7\u00e3o dos par\u00e2metros; sistemas n\u00e3o lineares; modelos b\u00e1sicos: o p\u00eandulo, o modelo predador-presa.<\/p>\n\n\n\n<p><strong>Cr\u00e9ditos:<\/strong>&nbsp; 6<\/p>\n\n\n\n<p><strong>Pr\u00e9-Requisitos:&nbsp;<\/strong>MA327 + MA211<\/p>\n\n\n\n<p><strong>Aula Te\u00f3rica:<\/strong><\/p>\n\n\n\n<ul><li>Seg: 19:00 &#8211; 21:00<\/li><li>Qua: 21:00 &#8211; 23:00<\/li><\/ul>\n\n\n\n<p><strong>Atendimento:<\/strong><\/p>\n\n\n\n<ul><li>Seg: 18:00 &#8211; 19:00 &#8211; PAD (Beatriz) &#8211; <a rel=\"noreferrer noopener\" aria-label=\"Link Permanente (abre numa nova aba)\" href=\"https:\/\/meet.google.com\/sza-onyx-vqt\" target=\"_blank\">Link Permanente<\/a><\/li><li>Qua: 18:00 &#8211; 19:00 &#8211; PED (Tiago) &#8211; <a href=\"https:\/\/meet.google.com\/ayf-fkaz-fae\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Link Permanente (abre numa nova aba)\">Link Permanente<\/a><\/li><\/ul>\n\n\n\n<p><strong>Listas de Exerc\u00edcios:<\/strong><\/p>\n\n\n\n<ul><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 1 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/1dguQY2_tB4q0txe0w07VJGmmDlxLEies\/view?usp=sharing\" target=\"_blank\">Lista 1<\/a> &#8211; (Exerc\u00edcios da Se\u00e7\u00e3o 1 do Dennis G. Zill)<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 2 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/1gOCXE_pAjq9s1olbaLH0yxrbQ8sJ7_y3\/view?usp=sharing\" target=\"_blank\">Lista 2<\/a> &#8211; Fator Integrante e EDO Separ\u00e1vel (Se\u00e7\u00f5es 2.2 e 2.3 do Dennis G. Zill)<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 3 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/1g_lsbWzok7vqRp6dwLW5nsdJ2BHLvsje\/view?usp=sharing\" target=\"_blank\">Lista 3<\/a> &#8211; An\u00e1lise Qualitativa (Se\u00e7\u00e3o 2.1 do Dennis G. Zill)<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 4 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/1ilqLiYKbhcWxWrpk0e4rKhGFuQsybWUE\/view?usp=sharing\" target=\"_blank\">Lista 4<\/a> &#8211; Modelos com EDO de 1a Ordem (Se\u00e7\u00f5es 2.4 e 2.5 do Dejairo &amp; Aloisio)<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 5 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/1vV_vhB6IZ43GHz6DQQ5R7t5Hi9ZhAUoR\/view?usp=sharing\" target=\"_blank\">Lista 5<\/a> &#8211; EDO Linear de 2a Ordem<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 6 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/1v_s9iWNAjwTlvTanJ70dEDrpIQT_5H_H\/view?usp=sharing\" target=\"_blank\">Lista 6<\/a> &#8211; EDO Linear de 2a Ordem<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 7 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/13ChVBTrwYdvLlg4gMarnbiC5YqPLmbRd\/view?usp=sharing\" target=\"_blank\">Lista 7<\/a> &#8211; Transformada de Laplace (Dennis)<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 8 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/13HORu-k8Z3w4x4sOA-ISF3zFC9zcZg6s\/view?usp=sharing\" target=\"_blank\">Lista 8<\/a> &#8211; Transformada de Laplace (Djairo)<\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Lista 9 (abre numa nova aba)\" href=\"https:\/\/drive.google.com\/file\/d\/1OVJrgAp5UTfADYY2WTDMohMDZHbAqkgs\/view?usp=sharing\" target=\"_blank\">Lista 9<\/a> &#8211; Sistemas de EDOs (Dennis)<\/li><li><a href=\"https:\/\/drive.google.com\/file\/d\/1OL_JtbIVPIOYEhN4Xgo7BRdSrenAITRm\/view?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Lista 10 (abre numa nova aba)\">Lista 10<\/a> &#8211; Sistemas de EDOs (Djairo)<\/li><\/ul>\n\n\n\n<p><strong>Avalia\u00e7\u00f5es:<\/strong><\/p>\n\n\n\n<ul><li><em>Atividade Avaliativa a ser entregue em  06\/10\/21 (Quarta-feira).<\/em><\/li><li>Prova 1: 06\/10\/21 (Quarta-feira)<\/li><li>Prova 2: 01\/12\/21 (Quarta-feira)<\/li><li>Prova 3 (Exame\/2a Chamada): 15\/12\/21 (Quarta-feira)<\/li><\/ul>\n\n\n\n<p><strong>C\u00e1lculo da M\u00e9dia e Conceito:<\/strong><\/p>\n\n\n\n<ol><li><em>C\u00e1lculo da <strong>P1<\/strong>: <\/em><br><em>P1=(A+2B)\/3, <\/em><br><em>onde A \u00e9 a nota da Atividade Avaliativa e B \u00e9 a nota da Prova do Dia 06\/10\/21.<\/em><br><\/li><li>C\u00e1lculo da <strong>M\u00e9dia Semestral<\/strong> (<strong>MS<\/strong>):<br> <strong>MS<\/strong> := <strong>(P1+P2) \/ 2<br><\/strong> <\/li><li>C\u00e1lculo da <strong>M\u00e9dia Final (MF)<\/strong><br>A P3, \u00e0 princ\u00edpio, \u00e9 optativa.<br>Se feita, ent\u00e3o MF:=(max {P1, P2}+P3)\/2;<br>sen\u00e3o, MF:=MS.<br><br>Est\u00e1 aprovado o aluno que tiver MF<strong>\u2265<\/strong>5!<\/li><\/ol>\n\n\n\n<p><strong>Bibliografia<\/strong><\/p>\n\n\n\n<ol><li>De Figueiredo, D. G., Neves, A. F., Equa\u00e7\u00f5es Diferenciais Aplicadas. 3\u00aa ed. Cole\u00e7\u00e3o Matem\u00e1tica Universit\u00e1ria, IMPA, 2015. <br><\/li><li>Dennis, G. Zill, Equa\u00e7\u00f5es Diferenciais com Aplica\u00e7\u00f5es em Modelagem (A First Course in Differential Equations with Modeling Applications), 10a ed., Cengage Learning, 2011.<br><\/li><li>Boyce, E.W., Diprima, R.C., Equa\u00e7\u00f5es Diferenciais Elementares e Problemas de Valores de Contorno, 10a ed., John Wiley Sons, 2012. <\/li><\/ol>\n\n\n\n<p><strong>Links \u00dateis:<\/strong><\/p>\n\n\n\n<ul><li><a rel=\"noreferrer noopener\" href=\"https:\/\/classroom.google.com\/\" target=\"_blank\">Google Sala de Aula<\/a><\/li><li><a rel=\"noreferrer noopener\" aria-label=\"Licen\u00e7a Mathematica (UNICAMP) (abre numa nova aba)\" href=\"https:\/\/www.citic.unicamp.br\/mathematica\" target=\"_blank\">Licen\u00e7a Mathematica (UNICAMP)<\/a><\/li><li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.wolframcloud.com\/\" target=\"_blank\">WolframCloud<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>MA 312&nbsp;&#8211; Turma&nbsp;Z Link Permanente do Meet: meet.google.com\/peb-dbji-wym O acesso a sala \u00e9 garantido somente se logado \u00e0 conta institucional da UNICAMP. Ementa: Equa\u00e7\u00f5es diferenciais de 1\u00aa ordem: equa\u00e7\u00f5es separ\u00e1veis, modelos b\u00e1sicos: din\u00e2mica de popula\u00e7\u00f5es, estabilidade, resfriamento de um corpo. &hellip; <a href=\"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/2021\/08\/09\/modelagem-matematica-e-equacoes-diferenciais\/\">Continue lendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":491,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[33,18],"tags":[],"_links":{"self":[{"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/posts\/1945"}],"collection":[{"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/comments?post=1945"}],"version-history":[{"count":18,"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/posts\/1945\/revisions"}],"predecessor-version":[{"id":2222,"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/posts\/1945\/revisions\/2222"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/media\/491"}],"wp:attachment":[{"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/media?parent=1945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/categories?post=1945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/index.php\/wp-json\/wp\/v2\/tags?post=1945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}