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<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/css/franklin.css"> <link rel=stylesheet href="/css/basic.css"> <link rel=icon href="/assets/favicon.png"> <title>404: File not found</title> <header> <a href="http://www.im.ufrj.br"><img style="max-height:60px; margin-top: 0px;" src="/assets/img/Logo_IM_caption.png"></a> <nav> <ul> <li><a href="/">Home</a> <li><a href="/pages/ensino/">Ensino</a> <li><a href="/pages/pesquisa/">Pesquisa</a> <li><a href="/pages/cv/">CV</a> <li><a href="/pages/blog/">Blog</a> <li><a href="/pages/contato/">Contato</a> <li><a href="/"><img alt=pt src="/assets/img/bandeira-nacional-brasil.jpg" width=16></a> <li><a href="/en/"><img alt=en src="/assets/img/usa1.jpg" width=16></a> </ul> <img src="/assets/hamburger.svg" id=menu-icon > </nav> <a href="http://www.ufrj.br"><img style="max-height:65px; margin-top: 0px;" src="/assets/img/001minerva_color_vert.png"></a> </header> <div class=franklin-content ><h1 id=404_file_not_found ><a href="#404_file_not_found" class=header-anchor >404: File not found</a></h1> <p>The requested file was not found.</p> <p>Please <a href="/">click here</a> to go to the home page.</p> <div class=page-foot > <div class=copyright > &copy; Ricardo M. S. Rosa. Last modified: March 18, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>. </div> </div> </div>
<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/css/franklin.css"> <link rel=stylesheet href="/css/basic.css"> <link rel=icon href="/assets/favicon.png"> <title>404: File not found</title> <header> <a href="http://www.im.ufrj.br"><img style="max-height:60px; margin-top: 0px;" src="/assets/img/Logo_IM_caption.png"></a> <nav> <ul> <li><a href="/">Home</a> <li><a href="/pages/ensino/">Ensino</a> <li><a href="/pages/pesquisa/">Pesquisa</a> <li><a href="/pages/cv/">CV</a> <li><a href="/pages/blog/">Blog</a> <li><a href="/pages/contato/">Contato</a> <li><a href="/"><img alt=pt src="/assets/img/bandeira-nacional-brasil.jpg" width=16></a> <li><a href="/en/"><img alt=en src="/assets/img/usa1.jpg" width=16></a> </ul> <img src="/assets/hamburger.svg" id=menu-icon > </nav> <a href="http://www.ufrj.br"><img style="max-height:65px; margin-top: 0px;" src="/assets/img/001minerva_color_vert.png"></a> </header> <div class=franklin-content ><h1 id=404_file_not_found ><a href="#404_file_not_found" class=header-anchor >404: File not found</a></h1> <p>The requested file was not found.</p> <p>Please <a href="/">click here</a> to go to the home page.</p> <div class=page-foot > <div class=copyright > &copy; Ricardo M. S. Rosa. Last modified: July 17, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>. </div> </div> </div>
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# Title: Computing time average bounds for the Van der Pol oscillator in Julia
# Publication date: 22 February 2021
# Last modified: March 18, 2024
# Last modified: July 17, 2024
# Code from https://rmsrosa.github.io/blog/2021/02/time_ave_bounds_vanderpol_in_Julia/

# Code snippet: vanderpolsolt.jl
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Failed to precompile PlotlyJS [f0f68f2c-4968-5e81-91da-67840de0976a] to "/home/runner/.julia/compiled/v1.10/PlotlyJS/jl_gm5S2j".
Failed to precompile PlotlyJS [f0f68f2c-4968-5e81-91da-67840de0976a] to "/home/runner/.julia/compiled/v1.10/PlotlyJS/jl_wPrQD1".
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{{ if pt_lang }}

#### ⟩⟩⟩ **Disciplina: Aspectos teóricos e numéricos de equações diferenciais estocásticas e aleatórias 2024/1**
#### ⟩⟩⟩ **Disciplina: Modelos generativos estocásticos 2024/2**

Veja aqui [informações sobre essa disciplina, período 2024/1](/pages/ensino/#20241_aspectos_teóricos_e_numéricos_de_equações_diferenciais_estocásticas_e_aleatórias) com [espelho na pós-graduação](/pages/ensino/#20241_aspectos_teóricos_e_numéricos_de_equações_diferenciais_estocásticas_e_aleatórias_-_pgmat).
Veja aqui [informações sobre essa disciplina, período 2024/2](/pages/ensino/#20242_modelos_generativos_estocásticos).

#### ⟩⟩⟩ **Disciplina: Equações Diferenciais 2024/1**
#### ⟩⟩⟩ **Disciplina: Álgebra Linear Avançada 2024/2**

Veja aqui [informações sobre a disciplina de Equações Diferenciais, período 2024/1](/pages/ensino/#20241_equações_diferenciais).
Veja aqui [informações sobre a disciplina de Álgebra Linear do Mestrado, período 2024/2](/pages/ensino/#20242_álgebra_linear_do_mestrado), com espelho na graduação [Álgebra Linear Avançada](/pages/ensino/#20242_álgebra_linear_avançada).

{{ else }}

### ⟩⟩⟩ Teaching: Stochastic and random ordinary differential equations
### ⟩⟩⟩ Teaching: Advanced Linear Algebra

I am teaching, for the third time, a course on theoretical and numerical aspects of stochastic and random ordinary differential equations. Lecture notes in Portuguese availabe at [rmsrosa.github.io/notas_sde](https://rmsrosa.github.io/notas_sde/).
I am teaching a graduate-level course on Linear Algebra. Lecture notes in Portuguese availabe at [Álgebra Linear Avançada - version 4/jan/2024](/assets/material/AlgebraLinearAvancada_RRosa_4jan2024.pdf).

### ⟩⟩⟩ Teaching: Differential equations
### ⟩⟩⟩ Teaching: Stochastic generative methods

I am also teaching the usual second-year undergraduate course on ordinary differential equations, with my lecture notes available in Portuguese at [Equações Diferenciais versão ago/2022](/assets/material/apostila-ed-ago2022.pdf).
I am also teaching a course on generative methods based on stochastic models, with my lecture notes available at [rmsrosa.github.io/random_notes/dev/generative/overview/](https://rmsrosa.github.io/random_notes/dev/generative/overview/).

{{ end }}

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<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/css/franklin.css"> <link rel=stylesheet href="/css/basic.css"> <link rel=icon href="/assets/favicon.png"> <title>Greetings</title> <header> <a href="http://www.im.ufrj.br"><img style="max-height:60px; margin-top: 0px;" src="/assets/img/Logo_IM_caption.png"></a> <nav> <ul> <li><a href="/en/">Home</a> <li><a href="/pages/teaching/">Teaching</a> <li><a href="/pages/research/">Research</a> <li><a href="/pages/cv_en/">CV</a> <li><a href="/pages/blog_en/">Blog</a> <li><a href="/pages/contact/">Contact</a> <li><a href="/"><img alt=pt src="/assets/img/bandeira-nacional-brasil.jpg" width=16></a> <li><a href="/en/"><img alt=en src="/assets/img/usa1.jpg" width=16></a> </ul> <img src="/assets/hamburger.svg" id=menu-icon > </nav> <a href="http://www.ufrj.br"><img style="max-height:65px; margin-top: 0px;" src="/assets/img/001minerva_color_vert.png"></a> </header> <div class=franklin-content ><h1 id=greetings ><a href="#greetings" class=header-anchor >Greetings</a></h1> <p>6 February 2021 | <strong>R. Rosa</strong></p> <p>This is an introductory post. I used to have a blog about homebrewing, created in 2006, in a time where not much information was available in Brazil about homebrewing. So I guess my blog turned out to be of some value. Since then, I was happy to see the homebrewing community grow so large in Brazil.</p> <p>Today, I decided to revive the blog, but open up the focus to include <em>more</em> math and coding &#40;yes, there were math in the homebrewing blog since brewing involves many physicochemical processes amenable to mathematical modeling&#41;. And to broaden the audience, I also decided, although with some reluctance, to write some posts in English, including this introductory one.</p> <p>For a long time, my personal homepages were all in pure html, sometimes with a little javascript. About two years ago, I revamped it in Python/Flask. Last year, though, I realized the power of <a href="https://julialang.org">the Julia language</a> and decided to rewrite my website in Julia/Franklin.</p> <p><a href="https://franklinjl.org">Franklin</a> is a static-site generator written purely in Julia, made by <a href="https://github.com/tlienart">Thibaut Lienart</a>. It is so much easier than Flask and good enough for me since I don&#39;t really need the power of Flask as building a dynamic site. In fact, in Flask, I ended up building a static site out of the dynamic one before publishing it.</p> <p>With Franklin, the only thing that was bothering me was that it seemed to me that I wouldn&#39;t be able to have comments on the blogs, since it is a static site. However, I ended up learning that there are a number of tools and apps to embed a comment section in static sites with javascripts or iframe. With that, Franklin turned out to be just perfect for what I need.</p> <p>Deploying the site is as simple as pushing the changes to a github repo. For the comments, there are paid and free apps, open and closed source. I chose to use <a href="https://utteranc.es">utterances</a>, a free, open-source, no-fuss solution, which is pretty easy to set up, and which keeps all the comments in another github repo &#40;one can use the same repo as that for the website, but I chose to use a different one, for more independence&#41;. One drawback is that to post a comment, one needs to have a github account. But I hope that will turn out not to be of too much trouble.</p> <p>Anyways, that is it for the Introduction.</p> <p>Cheers&#33;</p> <script src="https://utteranc.es/client.js" repo="rmsrosa/blog_comments" issue-term=pathname theme=github-light crossorigin=anonymous async> </script> <div class=page-foot > <div class=copyright > &copy; Ricardo M. S. Rosa. Last modified: March 18, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>. </div> </div> </div>
<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/css/franklin.css"> <link rel=stylesheet href="/css/basic.css"> <link rel=icon href="/assets/favicon.png"> <title>Greetings</title> <header> <a href="http://www.im.ufrj.br"><img style="max-height:60px; margin-top: 0px;" src="/assets/img/Logo_IM_caption.png"></a> <nav> <ul> <li><a href="/en/">Home</a> <li><a href="/pages/teaching/">Teaching</a> <li><a href="/pages/research/">Research</a> <li><a href="/pages/cv_en/">CV</a> <li><a href="/pages/blog_en/">Blog</a> <li><a href="/pages/contact/">Contact</a> <li><a href="/"><img alt=pt src="/assets/img/bandeira-nacional-brasil.jpg" width=16></a> <li><a href="/en/"><img alt=en src="/assets/img/usa1.jpg" width=16></a> </ul> <img src="/assets/hamburger.svg" id=menu-icon > </nav> <a href="http://www.ufrj.br"><img style="max-height:65px; margin-top: 0px;" src="/assets/img/001minerva_color_vert.png"></a> </header> <div class=franklin-content ><h1 id=greetings ><a href="#greetings" class=header-anchor >Greetings</a></h1> <p>6 February 2021 | <strong>R. Rosa</strong></p> <p>This is an introductory post. I used to have a blog about homebrewing, created in 2006, in a time where not much information was available in Brazil about homebrewing. So I guess my blog turned out to be of some value. Since then, I was happy to see the homebrewing community grow so large in Brazil.</p> <p>Today, I decided to revive the blog, but open up the focus to include <em>more</em> math and coding &#40;yes, there were math in the homebrewing blog since brewing involves many physicochemical processes amenable to mathematical modeling&#41;. And to broaden the audience, I also decided, although with some reluctance, to write some posts in English, including this introductory one.</p> <p>For a long time, my personal homepages were all in pure html, sometimes with a little javascript. About two years ago, I revamped it in Python/Flask. Last year, though, I realized the power of <a href="https://julialang.org">the Julia language</a> and decided to rewrite my website in Julia/Franklin.</p> <p><a href="https://franklinjl.org">Franklin</a> is a static-site generator written purely in Julia, made by <a href="https://github.com/tlienart">Thibaut Lienart</a>. It is so much easier than Flask and good enough for me since I don&#39;t really need the power of Flask as building a dynamic site. In fact, in Flask, I ended up building a static site out of the dynamic one before publishing it.</p> <p>With Franklin, the only thing that was bothering me was that it seemed to me that I wouldn&#39;t be able to have comments on the blogs, since it is a static site. However, I ended up learning that there are a number of tools and apps to embed a comment section in static sites with javascripts or iframe. With that, Franklin turned out to be just perfect for what I need.</p> <p>Deploying the site is as simple as pushing the changes to a github repo. For the comments, there are paid and free apps, open and closed source. I chose to use <a href="https://utteranc.es">utterances</a>, a free, open-source, no-fuss solution, which is pretty easy to set up, and which keeps all the comments in another github repo &#40;one can use the same repo as that for the website, but I chose to use a different one, for more independence&#41;. One drawback is that to post a comment, one needs to have a github account. But I hope that will turn out not to be of too much trouble.</p> <p>Anyways, that is it for the Introduction.</p> <p>Cheers&#33;</p> <script src="https://utteranc.es/client.js" repo="rmsrosa/blog_comments" issue-term=pathname theme=github-light crossorigin=anonymous async> </script> <div class=page-foot > <div class=copyright > &copy; Ricardo M. S. Rosa. Last modified: July 17, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>. </div> </div> </div>
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&copy; Ricardo M. S. Rosa. Last modified: March 18, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>.
&copy; Ricardo M. S. Rosa. Last modified: July 17, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>.
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<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/libs/katex/katex.min.css"> <link rel=stylesheet href="/libs/highlight/github.min.css"> <link rel=stylesheet href="/css/franklin.css"> <link rel=stylesheet href="/css/basic.css"> <link rel=icon href="/assets/favicon.png"> <title>Analytic solutions of RODEs</title> <header> <a href="http://www.im.ufrj.br"><img style="max-height:60px; margin-top: 0px;" src="/assets/img/Logo_IM_caption.png"></a> <nav> <ul> <li><a href="/en/">Home</a> <li><a href="/pages/teaching/">Teaching</a> <li><a href="/pages/research/">Research</a> <li><a href="/pages/cv_en/">CV</a> <li><a href="/pages/blog_en/">Blog</a> <li><a href="/pages/contact/">Contact</a> <li><a href="/"><img alt=pt src="/assets/img/bandeira-nacional-brasil.jpg" width=16></a> <li><a href="/en/"><img alt=en src="/assets/img/usa1.jpg" width=16></a> </ul> <img src="/assets/hamburger.svg" id=menu-icon > </nav> <a href="http://www.ufrj.br"><img style="max-height:65px; margin-top: 0px;" src="/assets/img/001minerva_color_vert.png"></a> </header> <div class=franklin-content ><h1 id=analytic_solutions_of_random_ordinary_differential_equations ><a href="#analytic_solutions_of_random_ordinary_differential_equations" class=header-anchor >Analytic solutions of random ordinary differential equations</a></h1> <p>6 Nov 2022 | <strong>R. Rosa</strong></p> <h2 id=introduction ><a href="#introduction" class=header-anchor >Introduction</a></h2> <p>Random ordinary differential equations are directly related to <a href="https://en.wikipedia.org/wiki/Stochastic_differential_equation">Stochastic differential equations</a> and are used in a number of models in a range of areas.</p> <p>As in many complicate differential equations, numerical methods are of fundamental importance in the understanding such models and in using them in applications.</p> <script src="https://utteranc.es/client.js" repo="rmsrosa/blog_comments" issue-term=pathname theme=github-light crossorigin=anonymous async> </script> <div class=page-foot > <div class=copyright > &copy; Ricardo M. S. Rosa. Last modified: March 18, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>. </div> </div> </div>
<!doctype html> <html lang=en > <meta charset=UTF-8 > <meta name=viewport content="width=device-width, initial-scale=1"> <link rel=stylesheet href="/libs/katex/katex.min.css"> <link rel=stylesheet href="/libs/highlight/github.min.css"> <link rel=stylesheet href="/css/franklin.css"> <link rel=stylesheet href="/css/basic.css"> <link rel=icon href="/assets/favicon.png"> <title>Analytic solutions of RODEs</title> <header> <a href="http://www.im.ufrj.br"><img style="max-height:60px; margin-top: 0px;" src="/assets/img/Logo_IM_caption.png"></a> <nav> <ul> <li><a href="/en/">Home</a> <li><a href="/pages/teaching/">Teaching</a> <li><a href="/pages/research/">Research</a> <li><a href="/pages/cv_en/">CV</a> <li><a href="/pages/blog_en/">Blog</a> <li><a href="/pages/contact/">Contact</a> <li><a href="/"><img alt=pt src="/assets/img/bandeira-nacional-brasil.jpg" width=16></a> <li><a href="/en/"><img alt=en src="/assets/img/usa1.jpg" width=16></a> </ul> <img src="/assets/hamburger.svg" id=menu-icon > </nav> <a href="http://www.ufrj.br"><img style="max-height:65px; margin-top: 0px;" src="/assets/img/001minerva_color_vert.png"></a> </header> <div class=franklin-content ><h1 id=analytic_solutions_of_random_ordinary_differential_equations ><a href="#analytic_solutions_of_random_ordinary_differential_equations" class=header-anchor >Analytic solutions of random ordinary differential equations</a></h1> <p>6 Nov 2022 | <strong>R. Rosa</strong></p> <h2 id=introduction ><a href="#introduction" class=header-anchor >Introduction</a></h2> <p>Random ordinary differential equations are directly related to <a href="https://en.wikipedia.org/wiki/Stochastic_differential_equation">Stochastic differential equations</a> and are used in a number of models in a range of areas.</p> <p>As in many complicate differential equations, numerical methods are of fundamental importance in the understanding such models and in using them in applications.</p> <script src="https://utteranc.es/client.js" repo="rmsrosa/blog_comments" issue-term=pathname theme=github-light crossorigin=anonymous async> </script> <div class=page-foot > <div class=copyright > &copy; Ricardo M. S. Rosa. Last modified: July 17, 2024. Built with <a href="https://github.com/tlienart/Franklin.jl">Franklin.jl</a>. </div> </div> </div>
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