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Davi C. Rodrigues
Aula 10\
\>", "Subtitle",
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e-mail: davi@cosmo-ufes.org
p\[AAcute]gina do curso: davi.cosmo-ufes.org/mc2019\
\>", "Text",
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Cell["\<\
Sobre  o uso e m\[EAcute]todos de resolu\[CCedilla]\[ATilde]o de problemas \
com NIntegrate, NDSolve, FindMinimum e NMinimize\
\>", "Chapter",
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Comecemos por um problema simples, que admite solu\[CCedilla]\[ATilde]o anal\
\[IAcute]tica.\
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Cell["\<\
Este \[EAcute] um problema simples que a solu\[CCedilla]\[ATilde]o anal\
\[IAcute]tica \[EAcute] tamb\[EAcute]m simples, mas usaremos este exemplo \
para ilustrar o emprego de m\[EAcute]todos num\[EAcute]ricos. E aqui teremos \
a vantagem de ser f\[AAcute]cil saber se a solu\[CCedilla]\[ATilde]o num\
\[EAcute]rica \[EAcute] boa ou n\[ATilde]o, pois j\[AAcute] temos a solu\
\[CCedilla]\[ATilde]o anal\[IAcute]tica.\
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Cell["\<\
O primeiro passo a notar \[EAcute] que n\[ATilde]o se pode fazer de imediato \
a integra\[CCedilla]\[ATilde]o num\[EAcute]rica... Relacionado a isso,  \
\[OpenCurlyDoubleQuote]Assumptions\[CloseCurlyDoubleQuote] n\[ATilde]o \
\[EAcute] compat\[IAcute]vel com NIntegrate.\
\>", "Text",
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Cell["\<\
Nota-se que \[EAcute] f\[AAcute]cil eliminar as constantes \[Rho]s e rs. 

- \[Rho]s \[EAcute] apenas uma constante multiplicativa, que pode ser \
facilmente inseria fora de NIntegrate.
- r pode ser reescalado, eliminando a depend\[EHat]ncia expl\[IAcute]cita em \
rs dentro da integral. 

Assim, temos 
\
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Usamos Rs s\[OAcute] para servir de lembra\[CCedilla]a de que a entrada de MN \
n\[ATilde]o ser\[AAcute] examenete a mesma de M, pois mudamos os limites de \
integra\[CCedilla]\[ATilde]o, r -> r rs => R -> Rs = R rs\
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Verificando o erro relativo, com rs=1, sem considerar a solu\[CCedilla]\
\[ATilde]o exata:\
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Cell["\<\
Qual seria a fonte do erro, a interpola\[CCedilla]\[ATilde]o ou a integra\
\[CCedilla]\[ATilde]o num\[EAcute]rica?
Para verificar se \[EAcute] erro da interpola\[CCedilla]\[ATilde]o, podemos \
facilmente aumentar o n\[UAcute]mero de pontos...\
\>", "Text",
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Pedimos 20 de precis\[ATilde]o, e ganhamos mais do que foi solicitado... Isso \
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Vale lembrar que o \[UAcute]ltimo teste acima comumente n\[ATilde]o pode ser \
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version GY-9:\n\n0.0503< r < 199.5\n0.0503 < rc <199.5\n0.1< \[Lambda] < 1000\
\n"
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