{"id":961,"date":"2025-06-20T17:25:09","date_gmt":"2025-06-20T17:25:09","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/?post_type=chapter&#038;p=961"},"modified":"2025-12-17T16:48:04","modified_gmt":"2025-12-17T16:48:04","slug":"applications-of-series-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/applications-of-series-apply-it\/","title":{"raw":"Applications of Series: Apply It","rendered":"Applications of Series: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Write out the terms in a binomial series<\/li>\r\n \t<li>Find the Taylor series for different functions<\/li>\r\n \t<li>Use Taylor series to solve differential equations<\/li>\r\n \t<li>Use Taylor series to evaluate integrals that don't have elementary antiderivatives<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h3>Taylor Series in Engineering: Analysis and Approximations<\/h3>\r\nYou're working as a consulting engineer for a technology company that designs various systems requiring precise mathematical modeling. Your team regularly encounters problems where standard analytical methods fall short, making Taylor series and power series techniques essential tools. Today, you're tackling four different projects: approximating square root calculations for a GPS system, modeling population growth with differential equations, evaluating complex integrals for signal processing, and analyzing pendulum motion for a precision timing device. Each project demonstrates how Taylor series transform impossible calculations into manageable engineering solutions.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313695[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313696[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313697[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313698[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Write out the terms in a binomial series<\/li>\n<li>Find the Taylor series for different functions<\/li>\n<li>Use Taylor series to solve differential equations<\/li>\n<li>Use Taylor series to evaluate integrals that don&#8217;t have elementary antiderivatives<\/li>\n<\/ul>\n<\/section>\n<h3>Taylor Series in Engineering: Analysis and Approximations<\/h3>\n<p>You&#8217;re working as a consulting engineer for a technology company that designs various systems requiring precise mathematical modeling. Your team regularly encounters problems where standard analytical methods fall short, making Taylor series and power series techniques essential tools. Today, you&#8217;re tackling four different projects: approximating square root calculations for a GPS system, modeling population growth with differential equations, evaluating complex integrals for signal processing, and analyzing pendulum motion for a precision timing device. Each project demonstrates how Taylor series transform impossible calculations into manageable engineering solutions.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313695\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313695&theme=lumen&iframe_resize_id=ohm313695&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313696\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313696&theme=lumen&iframe_resize_id=ohm313696&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313697\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313697&theme=lumen&iframe_resize_id=ohm313697&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313698\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313698&theme=lumen&iframe_resize_id=ohm313698&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":27,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":673,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/961"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":10,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/961\/revisions"}],"predecessor-version":[{"id":2517,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/961\/revisions\/2517"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/673"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/961\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=961"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=961"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=961"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}