{"id":42,"date":"2013-05-20T17:52:03","date_gmt":"2013-05-20T17:52:03","guid":{"rendered":"http:\/\/homepages.se.edu\/cmoretti\/?page_id=42"},"modified":"2019-10-28T15:42:41","modified_gmt":"2019-10-28T15:42:41","slug":"mathematica-notebooks-calculus-2","status":"publish","type":"page","link":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/","title":{"rendered":"Dr. Moretti&#8217;s Mathematica Notebooks &#8211; Calculus 2"},"content":{"rendered":"<h1 style=\"text-align: center\">Mathematica Notebooks for Calculus 2<\/h1>\n<p><span style=\"text-decoration: underline\">Important Note:<\/span>\u00a0The links for the notebooks open a new window or tab with a Google Drive page &#8211; the current settings for our homepages won&#8217;t allow me to host mathematica notebooks locally.<\/p>\n<h2>Taylor Polynomials<\/h2>\n<p>This notebook lets you look at the Taylor polynomials for a given function along with their graphs.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter  wp-image-102\" alt=\"taylor polynomials\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg\" width=\"500\" height=\"480\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg 1000w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials-300x288.jpg 300w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials-768x737.jpg 768w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImM25HdENKdGdFR3c&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 2 notebooks from Google Drive<\/a><\/p>\n<h2>Errors in using Taylor Polynomials<\/h2>\n<p>Most Taylor polynomials are only approximations for their functions &#8211; at each point away from the center there is usually an error, and the size of the error is predicted by the Taylor Remainder Theorem. \u00a0This notebook lets you graph and see a Taylor polynomial for a given function along with the error bounds predicted by the Remainder theorem. \u00a0The graph of the original function f(x) appears in purple, the graph of the Taylor polynomial in blue, and the region in which the original function f(x) must be based on the error estimates is shaded in purple. \u00a0The true graph of f(x) will always be in this region, but you can see that the farther away you get from the center of the approximation the wider this region gets (as the possible error gets larger). \u00a0By default for speed purposes a uniform bound for the derivatives involved in the error is used; you can deselect that in the manipulation (which gets significantly slower but reduces the size of the error bounds and makes the band where the function must be smaller).<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorerror.jpg\"><img decoding=\"async\" class=\"aligncenter  wp-image-101\" alt=\"taylor polynomials error bound\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorerror-922x1024.jpg\" width=\"461\" height=\"512\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorerror-922x1024.jpg 922w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorerror-270x300.jpg 270w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorerror-768x853.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorerror.jpg 1268w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImM25HdENKdGdFR3c&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 2 notebooks from Google Drive<\/a><\/p>\n<h2>Fourier Polynomials<\/h2>\n<p>This manipulation lets you compute Fourier polynomials on [-\u03c0,\u03c0] for a given function and their graphs.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fourierpolynomial.jpg\"><img decoding=\"async\" class=\"aligncenter  wp-image-104\" alt=\"fourier polynomial\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fourierpolynomial.jpg\" width=\"438\" height=\"428\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fourierpolynomial.jpg 1096w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fourierpolynomial-300x293.jpg 300w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fourierpolynomial-768x750.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fourierpolynomial-1024x1000.jpg 1024w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImM25HdENKdGdFR3c&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 2 notebooks from Google Drive<\/a><\/p>\n<h2>Fourier Polynomials and Sound<\/h2>\n<p>This notebook lets you explore the comparison to a function on [0,1] and its Fourier polynomial by converting them both into sounds you can play. \u00a0As you take more terms in the polynomial you can both see the graphs converge and hear the sounds converge.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fouriersound.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-100\" alt=\"fourier sound\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fouriersound.jpg\" width=\"501\" height=\"350\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fouriersound.jpg 1688w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fouriersound-300x210.jpg 300w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fouriersound-768x537.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fouriersound-1024x716.jpg 1024w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/fouriersound-1568x1096.jpg 1568w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImM25HdENKdGdFR3c&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 2 notebooks from Google Drive<\/a><\/p>\n<p><a title=\"Mathematica Notebook Library\" href=\"http:\/\/homepages.se.edu\/cmoretti\/main\/mathematicalibrarymain\/\">Back to my Mathematica Library<\/a><\/p>\n<p><a title=\"Dr. Christopher Moretti\u2019s Homepage\" href=\"http:\/\/homepages.se.edu\/cmoretti\/\">Back to my homepage<\/a><\/p>\n<p><a title=\"Southeastern main page\" href=\"http:\/\/www.se.edu\">Back to the Southeastern Main Page<\/a>\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mathematica Notebooks for Calculus 2 Important Note:\u00a0The links for the notebooks open a new window or tab with a Google Drive page &#8211; the current settings for our homepages won&#8217;t [&hellip;]<\/p>\n","protected":false},"author":24,"featured_media":0,"parent":19,"menu_order":0,"comment_status":"open","ping_status":"open","template":"page-templates\/page-with-sidebar.php","meta":{"footnotes":""},"class_list":["post-42","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Dr. Moretti&#039;s Mathematica Notebooks - Calculus 2 -<\/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:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Dr. Moretti&#039;s Mathematica Notebooks - Calculus 2 -\" \/>\n<meta property=\"og:description\" content=\"Mathematica Notebooks for Calculus 2 Important Note:\u00a0The links for the notebooks open a new window or tab with a Google Drive page &#8211; the current settings for our homepages won&#8217;t [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/\" \/>\n<meta property=\"article:modified_time\" content=\"2019-10-28T15:42:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/\",\"url\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/\",\"name\":\"Dr. Moretti's Mathematica Notebooks - Calculus 2 -\",\"isPartOf\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg\",\"datePublished\":\"2013-05-20T17:52:03+00:00\",\"dateModified\":\"2019-10-28T15:42:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#primaryimage\",\"url\":\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg\",\"contentUrl\":\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.se.edu\/cmoretti\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Dr. Moretti&#8217;s Mathematica Notebook Library\",\"item\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Dr. Moretti&#8217;s Mathematica Notebooks &#8211; Calculus 2\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.se.edu\/cmoretti\/#website\",\"url\":\"https:\/\/www.se.edu\/cmoretti\/\",\"name\":\"\",\"description\":\"Just another Southeastern Oklahoma State Sites site\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.se.edu\/cmoretti\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Dr. Moretti's Mathematica Notebooks - Calculus 2 -","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/","og_locale":"en_US","og_type":"article","og_title":"Dr. Moretti's Mathematica Notebooks - Calculus 2 -","og_description":"Mathematica Notebooks for Calculus 2 Important Note:\u00a0The links for the notebooks open a new window or tab with a Google Drive page &#8211; the current settings for our homepages won&#8217;t [&hellip;]","og_url":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/","article_modified_time":"2019-10-28T15:42:41+00:00","og_image":[{"url":"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg","type":"","width":"","height":""}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/","url":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/","name":"Dr. Moretti's Mathematica Notebooks - Calculus 2 -","isPartOf":{"@id":"https:\/\/www.se.edu\/cmoretti\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#primaryimage"},"image":{"@id":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#primaryimage"},"thumbnailUrl":"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg","datePublished":"2013-05-20T17:52:03+00:00","dateModified":"2019-10-28T15:42:41+00:00","breadcrumb":{"@id":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#primaryimage","url":"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg","contentUrl":"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/taylorpolynomials.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.se.edu\/cmoretti\/"},{"@type":"ListItem","position":2,"name":"Dr. Moretti&#8217;s Mathematica Notebook Library","item":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/"},{"@type":"ListItem","position":3,"name":"Dr. Moretti&#8217;s Mathematica Notebooks &#8211; Calculus 2"}]},{"@type":"WebSite","@id":"https:\/\/www.se.edu\/cmoretti\/#website","url":"https:\/\/www.se.edu\/cmoretti\/","name":"","description":"Just another Southeastern Oklahoma State Sites site","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.se.edu\/cmoretti\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/pages\/42","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/users\/24"}],"replies":[{"embeddable":true,"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/comments?post=42"}],"version-history":[{"count":1,"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/pages\/42\/revisions"}],"predecessor-version":[{"id":459,"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/pages\/42\/revisions\/459"}],"up":[{"embeddable":true,"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/pages\/19"}],"wp:attachment":[{"href":"https:\/\/www.se.edu\/cmoretti\/wp-json\/wp\/v2\/media?parent=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}