{"id":37,"date":"2013-05-23T18:45:41","date_gmt":"2013-05-23T18:45:41","guid":{"rendered":"http:\/\/homepages.se.edu\/cmoretti\/?page_id=37"},"modified":"2019-10-28T15:42:41","modified_gmt":"2019-10-28T15:42:41","slug":"mathematica-notebooks-calculus-1","status":"publish","type":"page","link":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/","title":{"rendered":"Dr. Moretti&#8217;s Mathematica Notebooks &#8211; Calculus 1"},"content":{"rendered":"<h1 style=\"text-align: center\">Mathematica Notebooks for Calculus 1<\/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>Epsilon-Delta definition of Limits<\/h2>\n<p>This notebook has a manipulation which lets you explore the\u00a0\u03b5-\u03b4 definition of limits. For the limit to exist no matter how narrow you make the gap between the horizontal red lines, you should be able to force the blue-shaded portion of the curve to be between them if you make the vertical blue lines sufficiently close together.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/limits.jpg\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter  wp-image-84\" alt=\"exploring limits\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/limits-926x1024.jpg\" width=\"463\" height=\"512\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Estimating Arclength<\/h2>\n<p style=\"text-align: left\">\u00a0This notebook lets you explore the definition and way to estimate arc length of a curve by adding the lengths of straight line segments.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingarclength.jpg\"><img decoding=\"async\" class=\"aligncenter  wp-image-91\" alt=\"estimating arclength\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingarclength-1024x1020.jpg\" width=\"512\" height=\"510\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingarclength-1024x1020.jpg 1024w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingarclength-150x150.jpg 150w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingarclength-300x300.jpg 300w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingarclength-768x765.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingarclength.jpg 1156w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Estimating The Graph of the Derivative<\/h2>\n<p>This notebook lets you explore the notion of the derivative as a function. \u00a0It lets you slide the tangent line along the graph of the original function and watch the graph of the derivative be constructed on the right.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/graphingthederivative.jpg\"><img decoding=\"async\" class=\"aligncenter  wp-image-88\" alt=\"graphingthederivative\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/graphingthederivative-1024x619.jpg\" width=\"512\" height=\"310\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Estimating Signed Areas by Riemann Sums<\/h2>\n<p style=\"text-align: left\">This notebook lets you explore the notion that the area under the curve can be found by approximating the region with rectangles and letting that area estimate get better and better by using more and more rectangles.<\/p>\n<p style=\"text-align: left\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/riemannsums.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-92\" alt=\"estimating areas\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/riemannsums-960x1024.jpg\" width=\"480\" height=\"512\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/riemannsums-960x1024.jpg 960w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/riemannsums-281x300.jpg 281w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/riemannsums-768x819.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/riemannsums.jpg 1148w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Volumes by Cross Sections<\/h2>\n<p>This notebook lets you explore the idea of finding volumes by cross-sections. \u00a0You pick the curves that form the &#8220;base&#8221; of the solid as well as the type of cross-sections (triangular, circular, etc.). \u00a0The manipulation then creates an approximation of the solid in 3D and computes the volume.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/volumebycrosssections.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-86\" alt=\"volume by cross sections\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/volumebycrosssections-746x1024.jpg\" width=\"373\" height=\"512\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Volumes of Revolution<\/h2>\n<p>This notebook lets you look at volumes of revolution &#8211; you can spin the region bounded by two curves around either the x-axis or y-axis.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/volumesofrevolution.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-93\" alt=\"volumes of revolution\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/volumesofrevolution-513x1024.jpg\" width=\"256\" height=\"512\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Area Functions<\/h2>\n<p>This notebook lets you graph an &#8220;area function&#8221; from calculus &#8211; that is, the graph of the signed area underneath a function <em>y<\/em>=<em>f(x)<\/em> from a starting point <em>x<\/em>=<em>a<\/em>. \u00a0This is a key idea behind the Fundamental Theorem of Calculus. \u00a0The areas under the graph of the original function are shaded with positive area being blue and negative area being red. \u00a0In the picture below you can see the area function (on bottom) beginning to decrease as in the top graph we are picking up negative area.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/areafunctions.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-87\" alt=\"area functions\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/areafunctions-794x1024.jpg\" width=\"397\" height=\"512\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Moving a Couch Around a Corner<\/h2>\n<p>This notebook demonstrates the process of moving a couch around an &#8220;L&#8221; corner so you find the longest couch that can make it around. \u00a0This couch is actually the\u00a0<em>shortest<\/em> of the ones that get stuck. \u00a0A version of this appears in the <a href=\"http:\/\/demonstrations.wolfram.com\/MovingACouchAroundACorner\/\" target=\"_blank\" rel=\"noopener noreferrer\">Wolfram Demonstrations Project<\/a>, and I wrote an article for the <a href=\"http:\/\/www.maa.org\/pubs\/cmj.html\" target=\"_blank\" rel=\"noopener noreferrer\">College Mathematics Journal<\/a> about how to find the longest couch in general.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/couch.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-85\" alt=\"moving a couch around a corner\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/couch-1024x937.jpg\" width=\"512\" height=\"469\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2>Sign Lines<\/h2>\n<p>Finding when a function is positive or negative is really an algebra problem, but it comes up in calculus (when the derivative is positive the original function is increasing, etc.). \u00a0While not foolproof, this notebook provides commands to attempt to construct a &#8220;sign line&#8221; for a given function (with a label). \u00a0It works best with algebra-oriented functions, and is very helpful when doing calculus-based graphing (in fact I wrote this to help write solutions to review sheets in Calculus 1). \u00a0The X&#8217;s in the picture below indicate an interval on which the function isn&#8217;t defined.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/signline.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-90\" style=\"border: 1px solid black\" alt=\"sign  lines\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/signline-1024x528.jpg\" width=\"512\" height=\"264\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/signline-1024x528.jpg 1024w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/signline-300x155.jpg 300w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/signline-768x396.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/signline.jpg 1124w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 notebooks from Google Drive<\/a><\/p>\n<h2 style=\"text-align: left\">The Mean Value Theorem<\/h2>\n<p>This notebook illustrates the Mean Value Theorem from calculus, which essentially states that under the right conditions when you have a function <em>f(x)<\/em> on the closed interval [<em>a,b<\/em>], there will be at least 1 point <em>x=c<\/em> in the interval where the tangent line to the curve will be parallel to the line joining the ends of the graph.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/meanvaluetheorem.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-89\" alt=\"mean value theorem\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/meanvaluetheorem-880x1024.jpg\" width=\"440\" height=\"512\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/meanvaluetheorem-880x1024.jpg 880w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/meanvaluetheorem-258x300.jpg 258w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/meanvaluetheorem-768x893.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/meanvaluetheorem.jpg 1224w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImUmhwc2loNTluR3M&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my Calculus 1 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 1 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-37","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 1 -<\/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-1\/\" \/>\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 1 -\" \/>\n<meta property=\"og:description\" content=\"Mathematica Notebooks for Calculus 1 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-1\/\" \/>\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\/limits-926x1024.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=\"4 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-1\/\",\"url\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/\",\"name\":\"Dr. Moretti's Mathematica Notebooks - Calculus 1 -\",\"isPartOf\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/limits-926x1024.jpg\",\"datePublished\":\"2013-05-23T18:45:41+00:00\",\"dateModified\":\"2019-10-28T15:42:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/#primaryimage\",\"url\":\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/limits.jpg\",\"contentUrl\":\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/limits.jpg\",\"width\":1238,\"height\":1368,\"caption\":\"\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-calculus-1\/#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; 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