{"id":11016,"date":"2024-05-28T15:58:12","date_gmt":"2024-05-28T15:58:12","guid":{"rendered":"https:\/\/milestone-institute.org\/modules\/differentiation\/"},"modified":"2026-07-31T10:22:59","modified_gmt":"2026-07-31T10:22:59","slug":"differentiation","status":"publish","type":"modules","link":"https:\/\/milestone-institute.org\/hu\/modules\/differentiation\/","title":{"rendered":"Differentiation"},"content":{"rendered":"<p><!-- MILESTONE MODULE PAGE \u2013 DIFFERENTIATION --><\/p>\n<section style=\"width: calc(100% - 40px); max-width: 1180px; margin: 48px auto 72px; box-sizing: border-box; font-family: inherit; color: #20252a;\" aria-labelledby=\"module-title\">\n<div style=\"overflow: hidden; background: #f7f4ea; border: 1px solid #d8d2c4; border-top: 10px solid #f4c94f; border-radius: 0 0 18px 18px; box-shadow: 0 18px 48px rgba(25,29,32,0.09);\">\n<p><!-- F\u0150 TARTALOM --><\/p>\n<div style=\"padding: clamp(34px,5vw,68px);\">\n<div style=\"display: flex; flex-wrap: wrap; gap: 10px; margin: 0 0 24px;\">\n<p><span style=\"display: inline-block; padding: 8px 14px; background: #f4c94f; border: 1px solid #d3aa2e; border-radius: 999px; font-size: 13px; line-height: 1; font-weight: bold; letter-spacing: 0.06em; text-transform: uppercase; color: #20252a;\"><br \/>\nNumerical Sciences<br \/>\n<\/span><\/p>\n<p><span style=\"display: inline-block; padding: 8px 14px; background: #fffdf7; border: 1px solid #cfc8b8; border-radius: 999px; font-size: 13px; line-height: 1; font-weight: bold; letter-spacing: 0.06em; text-transform: uppercase; color: #20252a;\"><br \/>\nImmersion 1<br \/>\n<\/span><\/p>\n<p><span style=\"display: inline-block; padding: 8px 14px; background: #fffdf7; border: 1px solid #cfc8b8; border-radius: 999px; font-size: 13px; line-height: 1; font-weight: bold; letter-spacing: 0.06em; text-transform: uppercase; color: #20252a;\"><br \/>\nMathematics and Its Applications<br \/>\n<\/span><\/p>\n<\/div>\n<h1 id=\"module-title\" style=\"margin: 0 0 22px; padding: 0; font-size: clamp(46px,6vw,78px); line-height: 0.98; letter-spacing: -0.035em; font-weight: bold; color: #20252a;\">\nDifferentiation<br \/>\n<\/h1>\n<div style=\"width: 76px; height: 4px; margin: 0 0 30px; background: #f4c94f; border-radius: 999px;\" aria-hidden=\"true\"><\/div>\n<p style=\"max-width: 980px; margin: 0; font-size: clamp(18px,1.55vw,24px); line-height: 1.62; font-weight: 400; color: #282d31;\">\nCalculus is an essential part of mathematics with rich applications in all fields of Numerical Sciences and beyond. It is amongst many countries&#8217; most important parts of mathematics for higher education. Consequently, a series of Milestone modules is designed to cover the necessary material, some of which is beyond the Hungarian curriculum.\n<\/p>\n<p style=\"max-width: 980px; margin: 24px 0 0; font-size: clamp(18px,1.55vw,24px); line-height: 1.62; font-weight: 400; color: #282d31;\">\nWhile the module builds from first principles and aims to prove the statements\u2014with the rigour allowed by the length of the classes\u2014we concentrate on the results, techniques and their applications so the module is accessible to a wider audience.\n<\/p>\n<div style=\"max-width: 980px; margin: 30px 0; padding: 20px 22px; background: #fffdf7; border-left: 6px solid #f4c94f; font-size: clamp(16px,1.2vw,19px); line-height: 1.6; color: #282d31;\">\n<strong>Good to know:<\/strong> The material is conceptually more difficult compared to the mathematics classes preceding these topics.\n<\/div>\n<p style=\"max-width: 980px; margin: 0; font-size: clamp(18px,1.55vw,24px); line-height: 1.62; font-weight: 400; color: #282d31;\">\nThe current module aims to familiarise students with the notion of differentiation starting from first principles, through the rules, up to the standard applications, including graph sketching, optimisation problems, approximating functions and roots.\n<\/p>\n<p style=\"max-width: 980px; margin: 24px 0 0; font-size: clamp(18px,1.55vw,24px); line-height: 1.62; font-weight: 400; color: #282d31;\">\nThe module is suitable for students with no or limited knowledge of the topic. The module is highly recommended for students interested in Numerical Sciences, but students interested in related fields from Natural Sciences are also welcome.\n<\/p>\n<\/div>\n<p><!-- MODULVEZET\u0150 --><\/p>\n<div style=\"display: flex; flex-wrap: wrap; background: #f4c94f; border-top: 1px solid #d3aa2e;\">\n<div style=\"flex: 1 1 260px; padding: 26px clamp(28px,4vw,52px); box-sizing: border-box;\">\n<div style=\"margin: 0 0 9px; font-size: 12px; line-height: 1.2; font-weight: 800; letter-spacing: 0.1em; text-transform: uppercase; color: #20252a;\">\nModule leader\n<\/div>\n<div style=\"max-width: 980px; font-size: clamp(17px,1.3vw,21px); line-height: 1.55; font-weight: 600; color: #20252a;\">\nSzab\u00f3 D\u00e1vid\n<\/div>\n<\/div>\n<\/div>\n<p><!-- VISSZAL\u00c9P\u00c9S --><\/p>\n<div style=\"padding: 22px clamp(28px,4vw,52px); background: #fffdf7; border-top: 1px solid #d8d2c4;\">\n<p><a style=\"display: inline-block; color: #20252a; font-size: 16px; line-height: 1.4; font-weight: bold; text-decoration: none; border-bottom: 2px solid #f4c94f; padding-bottom: 3px;\" href=\"https:\/\/milestone-institute.org\/modulkatalogus\/\"><br \/>\n\u2190 Vissza a modulkatal\u00f3gushoz<br \/>\n<\/a><\/p>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Calculus is a very important part of mathematics that has rich applications in all fields of Numerical Sciences and beyond. It is amongst the most important parts of mathematics for higher education for many countries. Consequently, a series of Milestone modules is designed to cover the necessary material some of which is beyond the Hungarian curriculum. While the module builds from first principles and aims to prove the statements (with the rigour allowed by length of the classes), we concentrate on the results, techniques and their applications so the module is accessible to a wider audience. In any case, students are warned that the material is conceptually more difficult compared to the mathematics classes preceding these topics.<br \/>\nThe aim of the current module is to familiarise students with the notion of differentiation starting from first principles, through the rules up the standard applications including graph sketching, optimisation problems, approximating functions and roots. The module is suitable for students with no or limited knowledge in the topic. The module is highly recommended for students interested in Numerical Sciences, but students interested in related fields from Natural Sciences are also welcome.<\/p>\n","protected":false},"featured_media":0,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"department":[],"division":[104],"terms_years":[252],"level":[245],"class_list":["post-11016","modules","type-modules","status-publish","format-standard","hentry","division-numerical-sciences","terms_years-2024-2025","level-immersion-1"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Differentiation &#8211; Milestone Institute<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/milestone-institute.org\/modules\/differentiation\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Differentiation &#8211; Milestone Institute\" \/>\n<meta property=\"og:description\" content=\"Calculus is a very important part of mathematics that has rich applications in all fields of Numerical Sciences and beyond. 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