{"id":4154,"date":"2025-10-16T15:27:38","date_gmt":"2025-10-16T15:27:38","guid":{"rendered":"http:\/\/wolframu.wolfram.com\/?post_type=courses&#038;p=4154"},"modified":"2026-08-24T18:35:29","modified_gmt":"2026-08-24T18:35:29","slug":"introduction-to-partial-differential-equations","status":"publish","type":"courses","link":"https:\/\/www.wolfram.com\/wolfram-u\/courses\/mathematics\/introduction-to-partial-differential-equations\/","title":{"rendered":"Introduction to Partial Differential Equations"},"content":{"rendered":"<p>This course introduces partial differential equations (PDEs) from scratch and covers the most important types of PDEs and their solution methods. The study of partial differential equations is a vital, dynamic and essential area of mathematics, with applications across physics, engineering and beyond. PDEs are used to describe many physical phenomena in fields such as fluid dynamics, electromagnetism, mechanics, classical optics and heat flow. Many fundamental laws of physics, including Maxwell's equations, the Navier\u2013Stokes equations, the heat equation, the wave equation and Schr\u00f6dinger's equation in quantum mechanics, are expressed in terms of PDEs. The course is designed to provide a user-friendly introduction to the theory and applications of PDEs, with interactive examples using Wolfram Language's powerful built-in solving methods. A prerelease version of this material is available as part of the <a href=\"https:\/\/www.wolfram-media.com\/products\/exploring-partial-differential-equations\/\" data-walid=\"WolframUCourse-IntroPDE-IntroPDEBook\">Wolfram eTextbook Series<\/a>. Wolfram AI Course Assistant is available for this interactive course.<\/p>\r\n\r\n","protected":false},"excerpt":{"rendered":"This course introduces partial differential equations (PDEs) from scratch and covers the most important types of PDEs and their solution methods. The study of partial differential equations is a vital, dynamic and essential area of mathematics, with applications across physics, engineering and beyond. PDEs are used to describe many physical phenomena in fields such as fluid dynamics, electromagnetism, mechanics, classical optics and heat flow. Many fundamental laws of physics, including Maxwell's equations, the Navier\u2013Stokes equations, the heat equation, the wave equation and Schr\u00f6dinger's equation in quantum mechanics, are expressed in terms of PDEs. The course is designed to provide a user-friendly introduction to the theory and applications of PDEs, with interactive examples using Wolfram Language's powerful built-in solving methods.","protected":false},"featured_media":4777,"parent":0,"template":"","meta":{"footnotes":""},"course_format":[19],"class_list":["post-4154","courses","type-courses","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/courses\/4154"}],"collection":[{"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/courses"}],"about":[{"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/types\/courses"}],"version-history":[{"count":3,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/courses\/4154\/revisions"}],"predecessor-version":[{"id":5352,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/courses\/4154\/revisions\/5352"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/media\/4777"}],"wp:attachment":[{"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/media?parent=4154"}],"wp:term":[{"taxonomy":"course_format","embeddable":true,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/course_format?post=4154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}