✎ calavancado []

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====== Cálculo Avançado (Verão 2022) ======

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Local e horário
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Segunda-Terça-Quinta-Sex (03 de janeiro a 11 de fevereiro, 16:00-18:05)

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Programa
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Aplicações diferenciáveis entre espaços Euclidianos. Derivada como transformação linear. O gradiente. Regra da cadeia.
Aplicações de classe $C^k$: Fórmula de Taylor. Teorema da função inversa; Formas locais de imersões e submersões. Funções
implícitas. Teorema do posto. Integrais múltiplas. Teorema de Fubini. Mudança de variáveis em integrais múltiplas.

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Bibliografia
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- M. Spivak, Cálculo em Variedades, Editora Ciência Moderna, 2003.
  - E. L. Lima, Análise no Espaço Rn, Coleção Matemática Universitária, Rio de Janeiro, IMPA, 2004.
  - E. L. Lima, Curso de Análise, Vol. 2, Rio de Janeiro, IMPA, Projeto Euclides, 1989.

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Critério de avaliação
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Listas de exercícios (com questões discursivas) e  avaliação final por questões-teste (via Google-docs).

<color #ed1c24>Crie uma pasta do seu drive com arquivos pdf de solução de exercícios e compartilhe o link na planilha</color> ([[https://docs.google.com/spreadsheets/d/1FzYGGvrtuaX_rC_dXid11gKpFZZiISER/edit#gid=1563607069|Lista]]) 
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Lista de Exercícios: [[https://drive.google.com/file/d/147GCpRWd-eT_LdjrgzWNG6jkeqftZWMu/view?usp=sharing|Lista 1]] (Prazo 15/01) , [[https://drive.google.com/file/d/1UzyPZifwqOHxAHwnc5JgeRqmTOTBf0sp/view?usp=sharing| Lista 2]] (Prazo 22/01), [[https://drive.google.com/file/d/1NQ0s1e20X48F0wcaQPdqnE49tVS3k6Ys/view?usp=sharing|Lista 3]] (Prazo 29/01)
[[https://drive.google.com/file/d/1-VnLwq8cP1Dd2q0Q4XZ0zzU0F49rPTUo/view?usp=sharing|Lista 4]] (Prazo 06/02)
[[https://drive.google.com/file/d/1vobholbo_0Mzv46Dc45PPA1TiZII5VEB/view?usp=sharing|Lista 5 (Prazo 11/02)]]
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 [[alglinear| Aula 1: Um pouco de Algebra linear]]
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 [[alglinear2| Aula 2: Ainda Algebra linear, posto e valores singulares]]
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 [[graficosnivel| Aula 3: gráficos e conjunto de nível]]
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 Aula 4: (Continuidade): [[https://drive.google.com/file/d/1VVuAcSxNUDE1LWlBFmUf1qlCV6-0JazG/view?usp=sharing|Video 1]], [[https://drive.google.com/file/d/1Ud4sc-wtm-eTT9rIEGNIMJybkfJsVG9E/view?usp=sharing|Video 2]], [[https://drive.google.com/file/d/1hFyEg8pUPezYk4GRy2RCW37vA5lOWKEH/view?usp=sharing|Notas]]
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 Aula 5: (Normas esquivalentes) [[https://drive.google.com/file/d/1moHofhLV34ntHmU08jB1eHAU-MBmkxcO/view?usp=sharing|Nota]]. , [[https://drive.google.com/file/d/1AWuNlWLuh9Lphwz5xSwQqQSHk48kKWeD/view?usp=sharing|Video]]
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 Aula 6: (Derivada) [[https://drive.google.com/file/d/1Qi0zfrve-ibhXhgzVIgkkNq-7qIxMHC7/view?usp=sharing|Nota]] [[https://drive.google.com/file/d/1XoPKkBgKT3PbvNKYyBCq6ZA7pUJwP5fz/view?usp=sharing|Video 1]], [[https://drive.google.com/file/d/1lEF_3mjY4L0ZE7EJzXkj3OSDxuNAvwC9/view?usp=sharing|Video 2]]
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Aula 7: Regra da Cadeia e Derivadas parciais, [[https://drive.google.com/file/d/1ryOWZYIY-Pr_ZRnFjJVtPTZgNUuduvdq/view?usp=sharing|Nota]] , [[https://drive.google.com/file/d/1YA_BcIispATq5IaH5HJ-XVeVUPAfPOi_/view?usp=sharing|Video 1]],
[[https://drive.google.com/file/d/1-Bs6lUvX1qm4jPMdlu4BLWS23UxsxAg0/view?usp=sharing|Video 2]]
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Aula 8: (Leibniz geral e bilineares) [[https://drive.google.com/file/d/1v5c6UT5AuXtXECLEFELmlDi_sSFzgCDt/view?usp=sharing|Nota 1]] , [[https://drive.google.com/file/d/1P5wrAfzns98VNUGh-kdhye0gH4UWq6Vx/view?usp=sharing|Nota 2]], [[https://drive.google.com/file/d/1TH0t1h6dS41XM8fDVUBVzXMqHHFE_hPW/view?usp=sharing|Video 1]],
[[https://drive.google.com/file/d/1infrzco5G4hJjI5-lf-lVF9m7dv2_rVR/view?usp=sharing|Video 2]],
[[https://drive.google.com/file/d/1pog0BgSL5fx_I0ohcyvvAW-4f-iuYEjl/view?usp=sharing|Video 3]],
[[https://drive.google.com/file/d/1_8DGmAHmh64fOVaWrEeXPMwdLAEw7NYP/view?usp=sharing|Video 4]]
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Aula 9: (TVM várias variáveis) [[https://drive.google.com/file/d/1jj188iWCgoNznLeWrqmV9HFWvNw5uwe2/view?usp=sharing|Nota]], [[https://drive.google.com/file/d/1nENN9HMqNodyG_5XxetXJj43ppGVZIU4/view?usp=sharing|Video]]
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Aula 10: Determinante e sua derivada [[https://drive.google.com/file/d/1ZO2aQv7UepoupaQXOgZNsBksUJNHkYE1/view?usp=sharing|Nota]],[[https://drive.google.com/file/d/1U31l_NbuIN7h9h7phgl_26kkUNrImIT_/view?usp=sharing|Video 1]]
[[https://drive.google.com/file/d/1OmjZPSO1r2ppr1b6oFji7JcRkDTI_KZy/view?usp=sharing|Video 2]]

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Aula 11: Segunda derivada, [[https://drive.google.com/file/d/1G8CFPuUAsOBwlYVw-pZvyEFrGRiJ0xQq/view?usp=sharing|Nota]] [[https://youtu.be/6QawLx6pq-c|Video 1]], [[https://youtu.be/U62yXWcnYF8|Video 2]]
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Aula 12: revisão e matrizes positive definite, [[https://drive.google.com/file/d/18Paky42XB36JVvnOML-sl-T2bZYCk2ff/view?usp=sharing|video]]
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Aula 13, 14: Teorema função implicita e sobre hipotese $C^1$, [[https://drive.google.com/file/d/1WRvB-t-QPmW6mgIesgv-RxAWhoEr_yLD/view?usp=sharing|Enunciar o teorema]], [[https://youtu.be/WM7Fb8XqZD4|Demonstração de TFImplicita]], [[https://drive.google.com/file/d/1QBYGzRsYYNQFiYuCOzGeB3it9H2ck0fj/view?usp=sharing|Exemplos]].  [[https://drive.google.com/file/d/1bTL3WF6PyEDKTxnPqTdElpZerXUDFBaI/view?usp=sharing|Nota completa]]
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Aula 15, Teorema da função inversa (usando implicita e equivalência) [[https://drive.google.com/file/d/1wHLovsmKOq1keRHJbOV0_0UniW9oDJWB/view?usp=sharing|video 1]], [[https://drive.google.com/file/d/1vS2eJNSnqJRYJQIUyTyQxfuadl9syWWb/view?usp=sharing|Video 2]] 
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Aula 16, Teorema do Posto, [[https://drive.google.com/file/d/1rtl7BKExTk57-iXOvVoHvSOsuKosNy8p/view?usp=sharing|video 1]], [[https://drive.google.com/file/d/1yaJkUiQLRnpt4TmF_DXOW5cSd94H8KWZ/view?usp=sharing|video 2]]
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Aula 17, Teorema do Posto continuação. [[https://drive.google.com/file/d/1TYZfYqU-UCEYjX5JWtxnK3Up5geB6aaq/view?usp=sharing|Nota]], [[https://drive.google.com/file/d/1qXt8_ZSXCrmmmS6nxIHfICF0xOQ_XzUi/view?usp=sharing|Video 1]], [[https://drive.google.com/file/d/1txw1CQ__YG9WCjMT9H-9xbVDuErPDZCo/view?usp=sharing|Video 2]]
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Aula 18, Integração, Teorema de Lebesgue-Riemann, [[https://drive.google.com/file/d/1x7tSKqCGO4x1CxbxDk9NtdKkcUfQZa9e/view?usp=sharing|Nota]] [[https://drive.google.com/file/d/1_eW6hZa5k_zQSxqLiI-6_cynALYp2oIJ/view?usp=sharing|Video 1]], [[https://drive.google.com/file/d/1txw1CQ__YG9WCjMT9H-9xbVDuErPDZCo/view?usp=sharing|Video 2]]
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Aula 19, Mudança de variáveis, [[https://drive.google.com/file/d/1Wis3h_5KfNZ9rZ1adSya4P1xpxYOZDTD/view?usp=sharing|Nota]], [[https://drive.google.com/file/d/1usNymkgYySBF6fG94a7E9R9W3gXt-kJ7/view?usp=sharing|Video 1]], [[https://drive.google.com/file/d/1g39lymq6CvCjJEAT-smAq2LfFqkWF_rZ/view?usp=sharing|Video 2]]
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