{"id":383,"date":"2024-03-11T16:50:43","date_gmt":"2024-03-11T19:50:43","guid":{"rendered":"https:\/\/cemeai.icmc.usp.br\/tiago\/?page_id=383"},"modified":"2024-03-25T13:46:50","modified_gmt":"2024-03-25T16:46:50","slug":"edo-verao-23","status":"publish","type":"page","link":"https:\/\/cemeai.icmc.usp.br\/tiago\/edo-verao-23\/","title":{"rendered":"EDO Ver\u00e3o 23"},"content":{"rendered":"\t\t
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EDO Ver\u00e3o 23<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Equa\u00e7\u00f5es Diferenciais Ordin\u00e1rias<\/span><\/p>

Ver\u00e3o 2023<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Professor:<\/strong> Tiago Pereira<\/span><\/p>

Atendimento: Ter\u00e7a-feira as 11h<\/span><\/p>

Sala: 3-242<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Monitor:<\/strong>\u00a0<\/span>Zheng Bian<\/span><\/a><\/span><\/p>

Atendimento: Quarta-feira as 10h<\/span><\/p>

Sala: 3-102<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Bibliografia<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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G Teschl – Ordinary Differential Equations and Dynamical Systems<\/p>

VI Arnold –\u00a0 Ordinary Differential Equations<\/p>

Augusto\u00a0 de Castro Jr – Curso de Equa\u00e7\u00f5es\u00a0 Diferenciais Ordin\u00e1rias<\/p><\/div>

Lista 1:<\/strong> Teschl Problemas Ch 1 & 2<\/p><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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AULA 1<\/h4>

Ch 1<\/strong><\/p>

No\u00e7\u00f5es preliminares, modelos, propriedades das equa\u00e7\u00f5es diferenciais, defini\u00e7\u00e3o de solu\u00e7\u00e3o, PVI.<\/p>

-modelos epidemiol\u00f3gicos SIS<\/p>

-modelos epidemiol\u00f3gicos \u2013 explos\u00e3o<\/p>

-Problema de Hubert – infinitas solu\u00e7\u00f5es<\/p>

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AULA 2\u00a0<\/h4>

Ch 2.2<\/strong><\/p>

Prova de Cauchy<\/span><\/p>

Teorema de Picard Lindeloef<\/span><\/p>

Enunciado e discuss\u00e3o<\/span><\/p>

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AULA 3<\/h4>

Ch 2.2<\/strong><\/p>

Prep para a Prova do Teorema de Picard<\/p>

(Contra) Exemplos de espa\u00e7os completos<\/p>

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AULA 4<\/h4>

Ch 2.4-5<\/strong><\/p>

Teorema do Pto fixo<\/p>

Prova do Teorema de Picard<\/p>

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AULA 5<\/h4>

Gronwall & Depend\u00eancia das condi\u00e7\u00f5es iniciais Prolongamento de solu\u00e7\u00e3o enunciado<\/p>

Discuss\u00e3o EDO com par\u00e2metros<\/p>

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AULA 6<\/h4>

Prova 1 \u2013 12 Jan<\/p>

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AULA 7<\/h4>

Ch 3.1<\/strong><\/p>

Sistemas Lineares aut\u00f4nomos<\/p>

Exponencial de Matriz e normas induzidas<\/p>

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AULA 8<\/h4>

Ch 3.2<\/strong><\/p>

Sistemas Lineares aut\u00f4nomos no plano<\/p>

Retratos de fase para sistemas lineares planares Pontos de sela, foco, no, centro<\/p>

Estabilidade de Lyapunov<\/p>

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AULA 9<\/h4>

Ch 3.4<\/strong><\/p>

Sistemas Lineares gerais<\/p>

Matrix fundamental e Propriedades<\/p>

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AULA 10<\/h4>

Ch 3.4<\/strong><\/p>

Varia\u00e7\u00e3o das constantes e formula de Liouville Aplica\u00e7\u00f5es<\/p>

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AULA 11<\/h4>

Ch 3.5<\/strong><\/p>

Sistemas Lineares Peri\u00f3dicos<\/p>

Monodromia e Teorema de Floquet<\/p>

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AULA 12<\/h4>

Ar\u2019d 28<\/strong><\/p>

Exemplos pendulo invertido<\/p>

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AULA 13<\/h4>

Exerc\u00edcios<\/p>

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AULA 14<\/h4>

Prova 2 \u2013 26 Jan<\/p>

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AULA 15<\/h4>

Ch 6.2-3<\/strong><\/p>

Fluxo e conjuntos invariantes (Zheng)<\/p>

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AULA 16<\/h4>

Ch 6.5<\/strong><\/p>

Estabilidade de pontos fixos e M\u00e9todo de Lyapunov<\/p>

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AULA 17<\/h4>

Ch 7.2<\/strong><\/p>

Variedades est\u00e1veis e inst\u00e1veis<\/p>

Dimens\u00e3o das variedades<\/p>

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AULA 18<\/h4>

Variedades est\u00e1veis e inst\u00e1veis \u2013 continua\u00e7\u00e3o<\/p>

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AULA 19<\/h4>

Prova 3 \u2013 3 Fev<\/p>

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AULA 20<\/h4>

Ch 6.4<\/strong><\/p>

Orbitas Peri\u00f3dicas<\/p>

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AULA 21<\/h4>

Arnold<\/strong><\/p>

Conjuga\u00e7\u00e3o. Exemplo com sistemas Lineares<\/p>

Hartman-Grobman enunciado<\/p>

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AULA 22<\/h4>

Ch 7.3<\/strong><\/p>

Hartman-Grobman Prova<\/p>

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AULA 23<\/h4>

Prova 4 \u2013 10 Fev<\/p>

\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

EDO Ver\u00e3o 23 Equa\u00e7\u00f5es Diferenciais Ordin\u00e1rias Ver\u00e3o 2023 Professor: Tiago Pereira Atendimento: Ter\u00e7a-feira as 11h Sala: 3-242 Monitor:\u00a0Zheng Bian Atendimento: Quarta-feira as 10h Sala: 3-102 Bibliografia G Teschl – Ordinary Differential Equations and Dynamical Systems VI Arnold –\u00a0 Ordinary Differential Equations Augusto\u00a0 de Castro Jr – Curso de Equa\u00e7\u00f5es\u00a0 Diferenciais Ordin\u00e1rias Lista 1: Teschl Problemas […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"class_list":["post-383","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages\/383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/comments?post=383"}],"version-history":[{"count":22,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages\/383\/revisions"}],"predecessor-version":[{"id":580,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages\/383\/revisions\/580"}],"wp:attachment":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/media?parent=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}