{"id":937,"date":"2025-06-20T17:23:40","date_gmt":"2025-06-20T17:23:40","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/?post_type=chapter&#038;p=937"},"modified":"2025-12-17T16:46:00","modified_gmt":"2025-12-17T16:46:00","slug":"operations-with-power-series-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/operations-with-power-series-apply-it\/","title":{"raw":"Operations with Power Series: Apply It","rendered":"Operations with Power Series: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Add and subtract power series<\/li>\r\n \t<li><span data-sheets-root=\"1\">Multiply two power series together<\/span><\/li>\r\n \t<li>Find derivatives of power series term by term<\/li>\r\n \t<li>Integrate power series term by term<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Power Series Operations<\/h2>\r\n<p class=\"whitespace-normal break-words\">Power series aren't just mathematical abstractions\u2014they're powerful tools used in engineering, physics, and data science to model complex systems and make accurate predictions. From designing smartphone processors to predicting weather patterns, understanding how to manipulate power series is essential for solving real-world problems.<\/p>\r\n<p class=\"whitespace-normal break-words\">Consider a data science team working on optimizing a streaming service's recommendation algorithm. They need to analyze user engagement patterns and predict viewing preferences using mathematical models based on power series representations.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313596[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313598[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313635[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313636[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Add and subtract power series<\/li>\n<li><span data-sheets-root=\"1\">Multiply two power series together<\/span><\/li>\n<li>Find derivatives of power series term by term<\/li>\n<li>Integrate power series term by term<\/li>\n<\/ul>\n<\/section>\n<h2>Power Series Operations<\/h2>\n<p class=\"whitespace-normal break-words\">Power series aren&#8217;t just mathematical abstractions\u2014they&#8217;re powerful tools used in engineering, physics, and data science to model complex systems and make accurate predictions. From designing smartphone processors to predicting weather patterns, understanding how to manipulate power series is essential for solving real-world problems.<\/p>\n<p class=\"whitespace-normal break-words\">Consider a data science team working on optimizing a streaming service&#8217;s recommendation algorithm. They need to analyze user engagement patterns and predict viewing preferences using mathematical models based on power series representations.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313596\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313596&theme=lumen&iframe_resize_id=ohm313596&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313598\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313598&theme=lumen&iframe_resize_id=ohm313598&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313635\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313635&theme=lumen&iframe_resize_id=ohm313635&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313636\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313636&theme=lumen&iframe_resize_id=ohm313636&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":15,"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\/937"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/937\/revisions"}],"predecessor-version":[{"id":2515,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/937\/revisions\/2515"}],"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\/937\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=937"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=937"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=937"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}