{"id":1799,"date":"2020-06-14T21:51:13","date_gmt":"2020-06-15T00:51:13","guid":{"rendered":"https:\/\/wp.ufpel.edu.br\/zahn\/?page_id=1799"},"modified":"2022-07-23T20:07:58","modified_gmt":"2022-07-23T23:07:58","slug":"mmxx-online","status":"publish","type":"page","link":"https:\/\/wp.ufpel.edu.br\/zahn\/disciplinas\/antiqua-archivum\/mmxx-online\/","title":{"rendered":"MMXX online"},"content":{"rendered":"

\u00a0MMXX – Formato online<\/strong><\/span><\/p>\n

MMXX – SEMESTER PRIMVM (pela segunda vez)<\/strong><\/span><\/p>\n

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Vari\u00e1veis Complexas<\/span><\/strong><\/span><\/p>\n

Plano de Ensino<\/a><\/p>\n

IMPORTANTE:<\/strong><\/span><\/p>\n

Acompanhamento da disciplina, informes, d\u00favidas, etc.: atrav\u00e9s do sistema e-aula<\/a> da UFPel.<\/p>\n

Tamb\u00e9m, teremos uma p\u00e1gina do Facebook, que pode ser acessada, clicando aqui<\/a>.<\/p>\n

Aulas gravadas: Ser\u00e3o liberadas no Youtube\u00a0<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0Aulas:<\/strong><\/h4>\n
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SEMANA I<\/strong><\/strong><\/span><\/span><\/p>\n

Aula 1.1<\/a><\/strong>:\u00a0Apresenta\u00e7\u00e3o do curso. N\u00fameros complexos como um corpo. Unidade imagin\u00e1ria e suas pot\u00eancias. Forma alg\u00e9brica. Imers\u00e3o de R em C.<\/span><\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 1.2<\/a><\/strong>:\u00a0Conjuga\u00e7\u00e3o e propriedades. Opera\u00e7\u00f5es em C.<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 1.3<\/a><\/strong>:\u00a0M\u00f3dulo de um n\u00famero complexo e propriedades.<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 2.1<\/a><\/strong>:\u00a0Proje\u00e7\u00e3o estereogr\u00e1fica – Parte I.<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 2.2<\/a><\/strong>:\u00a0Proje\u00e7\u00e3o estereogr\u00e1fica – Parte II.<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 2.3<\/a><\/strong>:\u00a0Forma trigonom\u00e9trica de um n\u00famero complexo e opera\u00e7\u00f5es.<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

SEMANA II<\/strong><\/p>\n

Aula 3.1<\/a><\/strong>: F\u00f3rmula de De Moivre.<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 3.1<\/a><\/strong>: Topologia em C – Parte I<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 3.3<\/a><\/strong>: Topologia em C – Parte II<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 4.1<\/a>:<\/strong> Topologia em C – Parte III<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

SEMANA III<\/strong><\/p>\n

Aula 4.2<\/a><\/strong>: Sequ\u00eancias em C, Parte I<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 4.3<\/a><\/strong>: Sequ\u00eancia em C, Parte II<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 5.1<\/a><\/strong>: Sequ\u00eancias em C, Parte III<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aula 5.2<\/a><\/strong>: S\u00e9ries complexas – Parte I<\/p>\n

_________________________________________________________________________<\/strong><\/p>\n

Aula 5.3<\/a><\/strong>: S\u00e9ries complexas – Parte II<\/p>\n

___________________________________________________________________________<\/strong><\/p>\n

SEMANA IV<\/strong><\/p>\n

Aula 6.1<\/a><\/strong>: Fun\u00e7\u00f5es de vari\u00e1vel complexa – primeiros conceitos.<\/p>\n

____________________________________________________________________________
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\nAula 6.2<\/a><\/strong>:\u00a0Fun\u00e7\u00f5es trigonom\u00e9tricas complexas e hiperb\u00f3licas complexas.
\n____________________________________________________________________________
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\nAula 6.3<\/a><\/strong>: \u00a0Fun\u00e7\u00f5es Complexas, Parte 3 [Fun\u00e7\u00e3o Log e seus ramos]
\n____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 6.4<\/a><\/strong>:\u00a0Um pouco mais sobre ramos de fun\u00e7\u00f5es plur\u00edvocas.
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Aula 7.1<\/a><\/strong>:\u00a0Propriedades do Log complexo. Fun\u00e7\u00f5es trigonom\u00e9tricas complexas inversas. Ramos.
____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 7.2<\/a><\/strong>: Limite de fun\u00e7\u00f5es complexas. Continuidade de fun\u00e7\u00f5es Complexas.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 7.3<\/strong><\/a>: Deriva\u00e7\u00e3o complexa. Fun\u00e7\u00f5es holomorfas \u2013 Parte I.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 8.1<\/strong><\/a>: Deriva\u00e7\u00e3o em C, Parte II (exemplos de aplica\u00e7\u00e3o das Eq. de Cauchy-Riemann, regras de deriva\u00e7\u00e3o em C, regra da Cadeia).<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 8.2<\/a><\/strong>: Deriva\u00e7\u00e3o em C, parte III. Transforma\u00e7\u00f5es b\u00e1sicas.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 8.3<\/a><\/strong>: Curvas no plano complexo.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 9.1<\/strong><\/a>: Integrais curvil\u00edneas.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aulas 9.2 e 9.3<\/a><\/strong>: Teorema da Primitiva.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 9.4<\/strong><\/a>: Teorema de Cauchy Goursat para regi\u00f5es multiplamente conexas.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 10.1<\/a><\/strong>: Teorema da f\u00f3rmula integral de Cauchy.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 10.2<\/strong><\/a>: Deriva\u00e7\u00e3o sob o s\u00edmbolo de integra\u00e7\u00e3o(F\u00f3rmula geral de Cauchy). Desigualdade de Cauchy.<\/p>\n

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Aula 11.1<\/strong><\/a>: Teoremas integrais (T. de Morera, T. de Liouville, T. Fund. da \u00c1lgebra)<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 11.2<\/strong><\/a>: Princ\u00edpio do m\u00f3dulo m\u00e1ximo.<\/p>\n

____________________________________________________________________________<\/strong><\/span><\/span><\/p>\n

Aula 12.1<\/a>:\u00a0Sequ\u00eancias de fun\u00e7\u00f5es complexas. Converg\u00eancia simples e uniforme. Teorema do crit\u00e9rio de Cauchy uniforme.
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\nAula 12.2<\/a>:\u00a0S\u00e9ries de fun\u00e7\u00f5es complexas, Parte I (conceito, converg\u00eancias simples, uniforme e absoluta, Teste M de Weiertrass, fun\u00e7\u00e3o zeta de Riemann, continuidade da soma de uma s\u00e9rie uniformemente convergente)<\/p>\n

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\nAula 13.1<\/a>:\u00a0S\u00e9ries de fun\u00e7\u00f5es, Parte II (deriva\u00e7\u00e3o termo a termo [de qualquer ordem] e integra\u00e7\u00e3o termo a termo de uma s\u00e9rie uniformemente convergente).<\/p>\n

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\nAula 13.2<\/a>:\u00a0S\u00e9ries de fun\u00e7\u00f5es, Parte III – S\u00e9ries de pot\u00eancias, Parte I (conceito, raio de converg\u00eancia e disco de Converg\u00eancia. Teorema de converg\u00eancia. F\u00f3rmula de Cauchy-Hadamard).<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

SEMANA X (de 30\/11 a 05\/12)<\/strong><\/p>\n

Aula 14.1<\/a>:\u00a0S\u00e9ries de fun\u00e7\u00f5es, Parte IV – S\u00e9ries de pot\u00eancias, parte II – S\u00e9rie de Taylor.<\/p>\n

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\nAula 14.2<\/a>:\u00a0S\u00e9ries de Fun\u00e7\u00f5es, Parte V (Produto e quociente de s\u00e9ries de pot\u00eancias).<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aulas 15.1+15.2<\/a>:\u00a0S\u00e9ries de fun\u00e7\u00f5es – Parte VI – S\u00e9ries de Laurent.<\/p>\n

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\n<\/strong>SEMANA XI<\/strong><\/p>\n

Aula 16.1+16.2<\/a>: Zeros e singularidades.<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aulas 17.1+17.2<\/a>: Res\u00edduos e Teorema dos res\u00edduos.<\/p>\n

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\n<\/strong>
\nAulas 18.1+18.2<\/a>: \u00a0Aplica\u00e7\u00f5es do teorema dos Res\u00edduos: integrais reais trigonom\u00e9tricas e integrais impr\u00f3prias.<\/p>\n

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\nSEMANA XII<\/strong><\/p>\n

Aulas 19.1+19.2<\/a>:\u00a0Integrais impr\u00f3prias usando res\u00edduos – Parte II<\/p>\n

____________________________________________________________________________<\/strong><\/p>\n

Aulas 20.1+20.2<\/a> [Final do curso]\u00a0Aula final do curso: Aplica\u00e7\u00f5es do Teorema dos Res\u00edduos – integrais impr\u00f3prias envolvendo fun\u00e7\u00f5es plur\u00edvocas.<\/p>\n

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Listas<\/strong><\/span><\/p>\n