{"id":685,"date":"2021-04-13T02:19:27","date_gmt":"2021-04-13T02:19:27","guid":{"rendered":"https:\/\/www.p-brane.com\/nm\/?p=685"},"modified":"2021-04-15T16:50:48","modified_gmt":"2021-04-15T16:50:48","slug":"wolfram-u-daily-study-group-calculus","status":"publish","type":"post","link":"https:\/\/www.p-brane.com\/nm\/wolfram-u-daily-study-group-calculus\/","title":{"rendered":"Wolfram U Daily Study Group: Calculus"},"content":{"rendered":"\n<p>The three week Calculus Study Group (4) uses the <a href=\"https:\/\/www.wolfram.com\/wolfram-u\/introduction-to-calculus\/\">Introduction to Calculus<\/a> self study course as part of the daily lectures and covers functions, limits, differential calculus, and integral calculus. This course is a good way to prepare for AP Calculus and is a great refresher on the topic.<\/p>\n\n\n\n<p>The functions 3<sup>x<\/sup>, the derivative of 3<sup>x<\/sup>, e<sup>x<\/sup>, the derivative of e<sup>x<\/sup>, and 2<sup>x<\/sup>, the derivative of 2<sup>x<\/sup>&nbsp;are shown in the plot on the left in the figure below to show the awesome properties of e<sup>x<\/sup>, for example. The derivative of e<sup>x<\/sup>&nbsp;is e<sup>x<\/sup>&nbsp;so the slope anywhere on the line is just the value of the function at that point.<\/p>\n\n\n\n<p>The tangent line and normal line are shown in the plot on the right for e<sup>x<\/sup>=3. This point was chosen as an example. The functions used to create the tangent and normal lines are as follows.<\/p>\n\n\n\n<ul><li>f(x)=e<sup>x<\/sup><\/li><li>Tangent(x)=f\u2032(x)(x\u2212x0)+f(x0) at x0=3<\/li><li>Normal(x)=(\u22121\/f\u2032(x))(x\u2212x0)+f(x0)\u00a0at x0=3<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_01.jpg\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"430\" src=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_01-1024x430.jpg\" alt=\"\" class=\"wp-image-709\" srcset=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_01-1024x430.jpg 1024w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_01-300x126.jpg 300w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_01-768x322.jpg 768w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_01-624x262.jpg 624w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_01.jpg 1167w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<p>The area under e<sup>x<\/sup>\u00a0to x0=3 can be found by integrating the curve from\u00a0\u2212\u221e\u00a0to 3 and is e<sup>3<\/sup>. Thus, the area under the curve is also the value of the function at that point.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_02.jpg\"><img decoding=\"async\" loading=\"lazy\" width=\"1000\" height=\"434\" src=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_02.jpg\" alt=\"\" class=\"wp-image-708\" srcset=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_02.jpg 1000w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_02-300x130.jpg 300w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_02-768x333.jpg 768w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/calc_graphic_02-624x271.jpg 624w\" sizes=\"(max-width: 1000px) 100vw, 1000px\" \/><\/a><\/figure>\n\n\n\n<p>To receive a program completion certificate you must pass three quizzes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-scaled.jpg\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"791\" src=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-1024x791.jpg\" alt=\"Wolfram Certificate of Program Completion, Jay Morreale has completed the online program Daily Study Group: Calculus.\" class=\"wp-image-674\" srcset=\"https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-1024x791.jpg 1024w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-300x232.jpg 300w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-768x593.jpg 768w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-1536x1187.jpg 1536w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-2048x1583.jpg 2048w, https:\/\/www.p-brane.com\/nm\/wp-content\/uploads\/2021\/04\/2020_08_calculus_certificate_completion-624x482.jpg 624w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption>Wolfram Certificate of Program Completion, Jay Morreale has completed the online program Daily Study Group: Calculus.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The three week Calculus Study Group (4) uses the Introduction to Calculus self study course as part of the daily lectures and covers functions, limits, differential calculus, and integral calculus. This course is a good way to prepare for AP Calculus and is a great refresher on the topic. The functions 3x, the derivative of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[75,72,84,83,85,69],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/posts\/685"}],"collection":[{"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/comments?post=685"}],"version-history":[{"count":6,"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/posts\/685\/revisions"}],"predecessor-version":[{"id":712,"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/posts\/685\/revisions\/712"}],"wp:attachment":[{"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/media?parent=685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/categories?post=685"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.p-brane.com\/nm\/wp-json\/wp\/v2\/tags?post=685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}