{"id":2692,"date":"2024-05-29T20:51:03","date_gmt":"2024-05-29T20:51:03","guid":{"rendered":"\/wolfram-u\/?post_type=courses&#038;p=2692"},"modified":"2026-08-24T18:23:54","modified_gmt":"2026-08-24T18:23:54","slug":"introduction-to-complex-analysis","status":"publish","type":"courses","link":"https:\/\/www.wolfram.com\/wolfram-u\/courses\/mathematics\/introduction-to-complex-analysis\/","title":{"rendered":"Introduction to Complex Analysis"},"content":{"rendered":"<p>This course provides a basic introduction to the properties and applications of complex numbers and functions with the help of visualization and computation tools in Wolfram Language. Complex analysis is a versatile tool that is used extensively in science, engineering and other fields. It is also a beautiful topic in itself. The course covers the complex plane; polar coordinates; complex, analytic and harmonic functions; Cauchy's theorem and integral formula; series representations; the residue theorem and application areas where complex analysis is used. The emphasis is on visualization and hands-on exercises, rather than on comprehensive proofs. A free ebook version of this material is available as part of the <a href=\"https:\/\/www.wolfram-media.com\/products\/essentials-of-complex-analysis\/\" data-walid=\"WolframUCourse-ComplexAnalysis-ComplexAnalysisBook\">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 provides a basic introduction to the properties and applications of complex numbers and functions with the help of visualization and computation tools in Wolfram Language. The course covers the elementary functions, the Cauchy\u2013Riemann equations, complex integration, Cauchy's theorem and the residue theorem.","protected":false},"featured_media":2968,"parent":0,"template":"","meta":{"footnotes":""},"course_format":[19],"class_list":["post-2692","courses","type-courses","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/courses\/2692"}],"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":4,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/courses\/2692\/revisions"}],"predecessor-version":[{"id":5119,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/courses\/2692\/revisions\/5119"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/media\/2968"}],"wp:attachment":[{"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/media?parent=2692"}],"wp:term":[{"taxonomy":"course_format","embeddable":true,"href":"https:\/\/www.wolfram.com\/wolfram-u\/wp-json\/wp\/v2\/course_format?post=2692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}