{"id":55,"date":"2022-09-07T16:04:32","date_gmt":"2022-09-07T16:04:32","guid":{"rendered":"https:\/\/www.unioviedo.es\/compnum\/?page_id=55"},"modified":"2024-01-12T20:31:43","modified_gmt":"2024-01-12T20:31:43","slug":"unit-4-numerical-differentiation-and-integration","status":"publish","type":"page","link":"https:\/\/www.unioviedo.es\/compnum\/index.php\/unit-4-numerical-differentiation-and-integration\/","title":{"rendered":"Unit 4. Numerical differentiation and integration"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"55\" class=\"elementor elementor-55\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-61ce04b2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"61ce04b2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2b60fd65\" data-id=\"2b60fd65\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2148bab elementor-widget elementor-widget-text-editor\" data-id=\"2148bab\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.7.4 - 31-08-2022 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#818a91;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#818a91;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<!-- wp:paragraph -->\n<p>1. Divided difference formulas<\/p>\n<!-- \/wp:paragraph --><!-- wp:paragraph -->\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex01.html\">Exercise 4.1.1:<\/a><\/strong> Forward, backward and centered formulas<\/p>\n<!-- \/wp:paragraph --><!-- wp:separator {\"align\":\"wide\"} --><hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\" \/><!-- \/wp:separator --><!-- wp:paragraph -->\n<p>2. Numerical differentiation using interpolation<\/p>\n<!-- \/wp:paragraph --><!-- wp:paragraph -->\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex02.html\">Exercise 4.2.1:<\/a><\/strong>\u00a0Order two formulas<\/p>\n<!-- \/wp:paragraph --><!-- wp:separator {\"align\":\"wide\"} --><hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\" \/><!-- \/wp:separator --><!-- wp:paragraph -->\n<p>3.\u00a0 Numerical differentiation of functions of two variables<\/p>\n<!-- \/wp:paragraph --><!-- wp:paragraph -->\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex04.html\">Exercise 4.3.1:<\/a><\/strong> Gradient and Hessian matrix<\/p>\n<!-- \/wp:paragraph --><!-- wp:separator {\"align\":\"wide\"} --><hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\" \/><!-- \/wp:separator --><!-- wp:paragraph -->\n<p>4. Quadrature formulas<br \/>\u00a0 \u00a0 Newton-Cotes formulas<\/p>\n<!-- \/wp:paragraph --><!-- wp:paragraph -->\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex06.html\">Exercise 4.4.1:<\/a><\/strong>\u00a0Midpoint and trapezoidal rules\u00a0<br \/><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex07.html\">Exercise 4.4.2:<\/a><\/strong>\u00a0Application of the quadrature rules<br \/><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex09.html\">Exercise 4.4.3:<\/a><\/strong>\u00a0Application of the composite rules<br \/><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex13.html\">Exercise 4.4.4:<\/a><\/strong>\u00a0Error of the Trapezoidal rule<br \/><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex14.html\">Exercise 4.4.5:<\/a><\/strong>\u00a0Error of the Trapezoidal rule<\/p>\n<!-- \/wp:paragraph --><!-- wp:separator {\"align\":\"wide\"} --><hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\" \/><!-- \/wp:separator --><!-- wp:paragraph -->\n<p>5. Gaussian formulas<\/p>\n<!-- \/wp:paragraph --><!-- wp:paragraph -->\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T4_Ex18.html\">Exercise 4.5.1<\/a><\/strong><\/p>\n<!-- \/wp:paragraph -->\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\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>1. Divided difference formulas Exercise 4.1.1: Forward, backward and centered formulas 2. Numerical differentiation using interpolation Exercise 4.2.1:\u00a0Order two formulas 3.\u00a0 Numerical differentiation of functions of two variables Exercise 4.3.1: Gradient and Hessian matrix 4. Quadrature formulas\u00a0 \u00a0 Newton-Cotes formulas Exercise 4.4.1:\u00a0Midpoint and trapezoidal rules\u00a0Exercise 4.4.2:\u00a0Application of the quadrature rulesExercise 4.4.3:\u00a0Application of the composite rulesExercise [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-55","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages\/55","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/comments?post=55"}],"version-history":[{"count":6,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages\/55\/revisions"}],"predecessor-version":[{"id":607,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages\/55\/revisions\/607"}],"wp:attachment":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/media?parent=55"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}