{"id":15636850,"url":"https://github.com/dpsanders/metodos_numericos_garantizados","last_synced_at":"2025-04-30T05:45:29.594Z","repository":{"id":73013978,"uuid":"119397255","full_name":"dpsanders/metodos_numericos_garantizados","owner":"dpsanders","description":"Curso de métodos numericos con intervalos, semestre 2018-2","archived":false,"fork":false,"pushed_at":"2018-05-14T17:09:14.000Z","size":2740,"stargazers_count":5,"open_issues_count":0,"forks_count":3,"subscribers_count":4,"default_branch":"master","last_synced_at":"2025-04-30T05:45:22.121Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/dpsanders.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2018-01-29T14:59:59.000Z","updated_at":"2022-01-23T05:29:29.000Z","dependencies_parsed_at":"2023-02-23T16:15:15.456Z","dependency_job_id":null,"html_url":"https://github.com/dpsanders/metodos_numericos_garantizados","commit_stats":{"total_commits":22,"total_committers":4,"mean_commits":5.5,"dds":0.4545454545454546,"last_synced_commit":"9b2f0bed4336fcc28a65b8613773c1e9756b0c8c"},"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/dpsanders%2Fmetodos_numericos_garantizados","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/dpsanders%2Fmetodos_numericos_garantizados/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/dpsanders%2Fmetodos_numericos_garantizados/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/dpsanders%2Fmetodos_numericos_garantizados/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/dpsanders","download_url":"https://codeload.github.com/dpsanders/metodos_numericos_garantizados/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":251651221,"owners_count":21621702,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-10-03T11:08:23.544Z","updated_at":"2025-04-30T05:45:29.572Z","avatar_url":"https://github.com/dpsanders.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Métodos numéricos garantizados con aplicaciones\n\n## Posgrado en Ciencias Físicas, UNAM\n\n- Tema selecto, semestre 2018-2\n\n- Profesores: Dr. Luis Benet (ICF) \u0026 Dr. David P. Sanders (FC)\n\n- 12 créditos; 6 horas a la semana\n\n- Horario: Lunes 12-15 y martes 11-14, Aula de Cómputo III, 2o. piso, Departamento de Física, Facultad de Ciencias\n\n## Objetivo\nEl objetivo del curso es introducir una serie de métodos modernos de la matemática y física computacionales que permiten calcular con conjuntos y establecer resultados\ngarantizados (rigurosos), a partir de cálculos numéricos con números de punto flotante.\n\nSe abordarán conceptos y técnicas\nrelacionados con la aritmética y análisis de intervalos, métodos tipo Newton, diferenciación automática, propagación de restricciones,\ny el método de integración de Taylor,  entre otros, y se cubrirán\ndistintas aplicaciones de interés en la ciencia computacional.\n\nLa implementación\nde estos métodos se llevará a cabo enfatizando aspectos modernos de los lenguajes de programación y el software libre.\n\nLas herramientas que se utilizarán en el curso incluyen los siguientes:\n\n- el lenguaje [Julia](http://www.julialang.org)\n- el sistema de control de versions `git`, y el sitio web [`GitHub`](http://www.github.com)\n- el notebook de [Jupyter](http://www.jupyter.org)\n\nSe enfatizarán tanto la parte matemática como la parte de la implementación computacional de los métodos.\n\n## Temario\n1. Programación en el lenguaje Julia y uso del notebook de Jupyter\n\n2. Aritmética de punto flotante y redondeo\n\n3. Aritmética de intervalos\n\n4. Funciones de intervalos\n\n5. Métodos de bisección y tipo Newton para calcular raíces de funciones\n\n6. Cuadratura numérica\n\n7. Optimización local y global\n\n8. Propagación de constricciones\n\n9. Diferenciación automática en una y varias variables\n\n10. Aproximación de funciones mediante modelos de Taylor\n\n11. Ecuaciones diferenciales ordinarias y el método de integración\nde Taylor\n\n\n## Bibliografía:\n\n- *L. Jaulin et al., *Applied Interval Analysis*, Springer, 2001\n\n- *W. Tucker, *Validated Numerics: A Short Introduction to Rigorous Computations*, Princeton\nUniversity Press, 2011\n\n- E. Hansen \u0026 G.W. Walster, *Global Optimization Using Interval Analysis*, 2a. edición, Marcel Dekker, 2004\n\n- R.E. Moore, R. Baker Kearfott \u0026 M.J. Cloud, *Introduction to Interval Analysis*, SIAM, 2009\n\n- G. Mayer, *Interval Analysis and Automatic Result Verification*, De Gruyter, 2017\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdpsanders%2Fmetodos_numericos_garantizados","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdpsanders%2Fmetodos_numericos_garantizados","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdpsanders%2Fmetodos_numericos_garantizados/lists"}