{"id":233,"date":"2019-03-16T04:28:37","date_gmt":"2019-03-16T04:28:37","guid":{"rendered":"http:\/\/sites.monroecc.edu\/multivariablecalculus\/?page_id=233"},"modified":"2023-06-16T20:19:52","modified_gmt":"2023-06-16T20:19:52","slug":"geogebra-visualizations","status":"publish","type":"page","link":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/geogebra-visualizations\/","title":{"rendered":"Geogebra Visualizations"},"content":{"rendered":"<h1>Geogebra Visualizations<\/h1>\n<h2><strong>Geogebra Apps for Algebra:<\/strong><\/h2>\n<ul><li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/wcepsqqy\" target=\"_blank\" rel=\"noreferrer noopener\">Point Coordinate Practice<\/a><\/li>\n<\/ul><h2>Geogebra Apps for Calculus:<\/h2>\n<ul><li>\n<h3>Area\/Accumulation Functions<\/h3>\n<ul><li><a href=\"https:\/\/www.geogebra.org\/m\/vy5cfdug\" target=\"_blank\" rel=\"noreferrer noopener\">Accumulation Function Exploration Tool<\/a><br>\nA tool to explore the accumulation function version of the Fundamental Theorem of Calculus.<\/li>\n\t<li><a href=\"https:\/\/www.geogebra.org\/m\/r6raanjp\" target=\"_blank\" rel=\"noreferrer noopener\">Accumulation Function Curve Sketching Example 1<\/a><br>\nBuilding an antiderivative accumulation function from a piece-wise derivative graph.<\/li>\n<\/ul><\/li>\n<\/ul><h2>Geogebra Apps for Differential Equations:<\/h2>\n<ul><li>\n<h3>Bifurcation Motivation<\/h3>\n<ul><li><a href=\"https:\/\/www.geogebra.org\/m\/ubrrxnx8\" target=\"_blank\" rel=\"noreferrer noopener\">Example 1<\/a>, $\\dfrac{dy}{dt} = y^2 + 2y + a$,\u00a0 Dynamic graph of $f(y) = y&#8217;$ to illustrate Bifurcation<\/li>\n<\/ul><\/li>\n\t<li>\n<h3>Bifurcation Diagrams<\/h3>\n<ul><li><a href=\"https:\/\/www.geogebra.org\/m\/eqtydqdq\" target=\"_blank\" rel=\"noreferrer noopener\">Example 1<\/a>, $\\dfrac{dy}{dt} = y^2 + 2y + a$,\u00a0 Bifurcation Diagram<br>\nby Paul Seeburger<\/li>\n\t<li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/jufntewh\" target=\"_blank\" rel=\"noreferrer noopener\">Bifurcation diagram for: $\\dfrac{dy}{dt} =\\frac{1}{50}(y^2 + ay + 16)$<\/a>\u00a0<br>\nby Paul Seeburger<\/li>\n\t<li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/efrpenbg\" target=\"_blank\" rel=\"noreferrer noopener\">Saddle Node Bifurcation: y&#8217; = y<sup>2<\/sup> + a<\/a><br>\nAdapted from an app by Pablo Rodr\u00edguez S\u00e1nchez.<\/li>\n\t<li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/c9ypcjc9\" target=\"_blank\" rel=\"noreferrer noopener\">Pitchfork Bifurcation: y&#8217; = y(a &#8211; y<sup>2<\/sup>)<\/a><br>\nAdapted from an app by Pablo Rodr\u00edguez S\u00e1nchez.<\/li>\n\t<li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/kbecqm8k\" target=\"_blank\" rel=\"noreferrer noopener\">Bifurcation diagram for: y&#8217; = y<sup>3<\/sup> &#8211; ay<sup>2<\/sup><\/a><br>\nNew example adapted from an app by Pablo Rodr\u00edguez S\u00e1nchez.<\/li>\n<\/ul><\/li>\n\t<li>\n<h3>Second-order Slope Fields and Solution Curves<\/h3>\n<ul><li><a href=\"https:\/\/www.geogebra.org\/m\/fz4pctru\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"font-family:'times new roman', times, serif\"><em>y<\/em><\/span>&#8221; \u2212 9<span style=\"font-family:'times new roman', times, serif\"><em>y<\/em><\/span> = 0<\/a><\/li>\n\t<li><a href=\"https:\/\/www.geogebra.org\/m\/ypy76kpr\" target=\"_blank\" rel=\"noreferrer noopener\">2<span style=\"font-family:'times new roman', times, serif\"><em>y<\/em><\/span>&#8221; \u2212 5<span style=\"font-family:'times new roman', times, serif\"><em>y<\/em><\/span>&#8216; \u2212 3<span style=\"font-family:'times new roman', times, serif\"><em>y<\/em><\/span><em>\u00a0<\/em>= 0<\/a><\/li>\n\t<li><a href=\"https:\/\/www.geogebra.org\/m\/uu5hxkw9\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"font-family:'times new roman', times, serif\"><em>y<\/em><\/span>&#8221; + 4<span style=\"font-family:'times new roman', times, serif\"><em>y&#8217;<\/em><\/span>\u00a0+ 3<span style=\"font-family:'times new roman', times, serif\"><em>y<\/em><\/span> = 0<\/a><\/li>\n<\/ul><\/li>\n\t<li>\n<h3>Second-order Repeated Root Solutions<\/h3>\n<ul><li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/n7byxebf\" target=\"_blank\" rel=\"noreferrer noopener\">Homogeneous case<\/a><\/li>\n\t<li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/qxxh2rw9\" target=\"_blank\" rel=\"noreferrer noopener\">Nonhomogeneous case: <span style=\"font-family:'times new roman', times, serif\"><em>g<\/em><\/span>(<span style=\"font-family:'times new roman', times, serif\"><em>x<\/em><\/span>) = <em><span style=\"font-family:'times new roman', times, serif\">x<\/span><\/em> &#8211; 2<\/a><\/li>\n\t<li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/wmtf9fj9\" target=\"_blank\" rel=\"noreferrer noopener\">Nonhomogeneous case: <span style=\"font-family:'times new roman', times, serif\"><em>g<\/em><\/span>(<span style=\"font-family:'times new roman', times, serif\"><em>x<\/em><\/span>) = 2sin <span style=\"font-family:'times new roman', times, serif\"><em>x<\/em><\/span><\/a><\/li>\n\t<li><a title=\"Opens external link in new window\" href=\"https:\/\/www.geogebra.org\/m\/gurxmxtw\" target=\"_blank\" rel=\"noreferrer noopener\">Nonhomogeneous case: <span style=\"font-family:'times new roman', times, serif\"><em>g<\/em><\/span>(<span style=\"font-family:'times new roman', times, serif\"><em>x<\/em><\/span>) = 2<span style=\"font-family:'times new roman', times, serif\"><em>e<sup>x<\/sup><\/em><\/span><\/a><\/li>\n<\/ul><\/li>\n\t<li>\n<h3>Free and Forced Spring Motion<\/h3>\n<ul><li><a href=\"https:\/\/www.geogebra.org\/m\/ykqc5be6\" target=\"_blank\" rel=\"noreferrer noopener\">Spring Motion Demonstration (with\/without Forcing)<\/a><\/li>\n<\/ul><\/li>\n\t<li>\n<h3>Laplace Transforms<\/h3>\n<ul><li><a href=\"https:\/\/www.geogebra.org\/m\/usn9espf\" target=\"_blank\" rel=\"noreferrer noopener\">Interactive Piecewise Function Plotter with the Unit Step Function<\/a><\/li>\n<\/ul><\/li>\n\t<li>\n<h3>Phase Portraits for Systems of Differential Equations<\/h3>\n<ul><li><a href=\"https:\/\/www.geogebra.org\/m\/xzshp8u5\" target=\"_blank\" rel=\"noreferrer noopener\">Example 1, Saddle Point<\/a><\/li>\n\t<li><a href=\"https:\/\/www.geogebra.org\/m\/nes6uxwf\" target=\"_blank\" rel=\"noreferrer noopener\">DE System Explorer<\/a>, allows you to see the phase portrait of any 2 x 2 linear system of ODEs.\u00a0<\/li>\n<\/ul><\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Geogebra Visualizations Geogebra Apps for Algebra: Point Coordinate Practice Geogebra Apps for Calculus: Area\/Accumulation Functions Accumulation Function Exploration Tool A tool to explore the accumulation function version of the Fundamental Theorem of Calculus. Accumulation Function Curve Sketching Example 1 Building an antiderivative accumulation function from a piece-wise derivative graph. Geogebra Apps for Differential Equations: Bifurcation [&#8230;]<\/p>\n","protected":false},"author":654,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-233","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages\/233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/users\/654"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/comments?post=233"}],"version-history":[{"count":24,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages\/233\/revisions"}],"predecessor-version":[{"id":454,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages\/233\/revisions\/454"}],"wp:attachment":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/media?parent=233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}