{"id":4921,"date":"2022-02-02T08:30:07","date_gmt":"2022-02-02T07:30:07","guid":{"rendered":"https:\/\/lyon-geologie.univ-lyon1.fr\/?page_id=4921"},"modified":"2023-02-28T14:08:01","modified_gmt":"2023-02-28T13:08:01","slug":"l3g_math2","status":"publish","type":"page","link":"https:\/\/lyongeologie.fr\/en\/l3-geosciences\/l3g_math2\/","title":{"rendered":"L3G Math\u00e9matiques 2"},"content":{"rendered":"
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Mathematics 2
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3 Credits<\/em><\/p>

Contact: Fr\u00e9d\u00e9ric CHAMBAT<\/a>
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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tBack to the previous page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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Ce cours vise \u00e0 approfondir les concepts math\u00e9matiques d\u00e9velopp\u00e9s au premier semestre afin de pouvoir aborder ensuite la m\u00e9canique des fluides, l\u2019\u00e9lasticit\u00e9, le g\u00e9omagn\u00e9tisme, la sismologie etc.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Une divergence, c'est un flux sortant. <\/small><\/i><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Contents:<\/strong><\/p>

  • Les fonctions de plusieurs variables II<\/strong>, l\u2019int\u00e9gration, 4 h : D\u00e9rivation d\u2019une int\u00e9grale simple. D\u00e9rivation sous le signe int\u00e9gral. Cas mixte. Int\u00e9grales doubles ou triples. Th\u00e9or\u00e8me de Fubini. Changement de variables.<\/li>
  • Les op\u00e9rateurs de d\u00e9rivation II<\/strong> – 8 h : Le gradient, la divergence, le rotationnel, le Laplacien : d\u00e9finitions int\u00e9grales et lien avec les d\u00e9finitions locales. Le produit vectoriel, le tenseur altern\u00e9. La circulation. Le laplacien vectoriel. Le gradient d\u2019un vecteur. La notation indicielle. Utilisation en coordonn\u00e9es cylindrique et sph\u00e9rique. Conditions pour grad, div, rot nuls. Th\u00e9or\u00e8me de d\u00e9composition de Helmholtz-Hodge<\/li>
  • \u00c9quations fondamentales de la physique<\/strong> et quelques solutions 4 h : Les ondes. La diffusion. Equation de Poisson, de Laplace.<\/li>
  • Les harmoniques sph\u00e9riques<\/strong> 4 h : Solutions de l\u2019\u00e9quation de Laplace. Base des fonctions d\u00e9finies sur la sph\u00e8re<\/li>
  • Introduction aux tenseurs<\/strong> 4 h : D\u00e9finitions. Propri\u00e9t\u00e9s. Calcul indiciel. D\u00e9riv\u00e9e d\u2019un champ de tenseurs. Ex : le tenseur des contraintes, le tenseur des coefficients \u00e9lastiques (propri\u00e9t\u00e9s et manipulations math\u00e9matiques; la physique sera faite dans le cours d\u2019\u00e9lasticit\u00e9)<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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    \n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"

    Math\u00e9matiques 2 Cr\u00e9dits : 3 ECTS Responsable : Fr\u00e9d\u00e9ric CHAMBAT Retour \u00e0 la liste des UEs Ce cours vise \u00e0 approfondir les concepts math\u00e9matiques d\u00e9velopp\u00e9s au premier semestre afin de pouvoir aborder ensuite la m\u00e9canique des fluides, l\u2019\u00e9lasticit\u00e9, le g\u00e9omagn\u00e9tisme, la sismologie etc. Une divergence, c’est un flux sortant. Contenu : Les fonctions de plusieurs […]<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":489,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-4921","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/pages\/4921","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/comments?post=4921"}],"version-history":[{"count":24,"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/pages\/4921\/revisions"}],"predecessor-version":[{"id":16713,"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/pages\/4921\/revisions\/16713"}],"up":[{"embeddable":true,"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/pages\/489"}],"wp:attachment":[{"href":"https:\/\/lyongeologie.fr\/en\/wp-json\/wp\/v2\/media?parent=4921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}