Department of Mathematics and Statistics, Binghamton University calculus:resources:calculus_flipped_resources https://www2.math.binghamton.edu/ 2026-04-08T10:46:06-04:00 FeedCreator 1.7.2-ppt DokuWiki Applications: Flipped Calculus at Binghamton SUNY 2015-08-28T22:35:15-04:00 2015-08-28T22:35:15-04:00 https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications <p> <style> #header { background-color:#006f3f; height: 55px; font-size: 21px; font-weight: bold; text-align: center; color: rgb(256,256,256) } #menu { height: 35px; font-size: 15px; font-family: Tahoma, Geneva, sans-serif; font-weight: bold; text-align: center; text-shadow: 3px 2px 3px #333333; background-color: rgb(102,156,156); } #menu ul { height: auto; padding: 8px 0px; margin: 0px; } #menu li { display: inline; padding: 16px; } #menu a { text-decoration: none; color: rgb(256,256,256); padding: 8px 8px 8px 8px; } #menu a:hover { color: #006f3f; background-color: #FFF; } </style> <div id="header"> <h1 style="margin-top:1; margin-bottom:1;">Flipped Calculus 1 at Binghamton</h1></div> <div id="menu"> <ul> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources">Home</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits">Limits</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives">Derivatives</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications">Applications</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals">Integrals</a></li> </ul> </div> <br/> </p> <!-- EDIT1 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT3 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit5" id="linearization_and_differentials">Linearization and Differentials</h2> <!-- EDIT5 SECTION "Linearization and Differentials" [1548-] --></div><!-- EDIT4 PLUGIN_WRAP_END [0-] --><!-- EDIT6 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT8 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/1rtvN3dcxbU" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT9 PLUGIN_WRAP_END [0-] --><!-- EDIT10 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/2bf00We0FNg" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT11 PLUGIN_WRAP_END [0-] --></div><!-- EDIT7 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT12 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT14 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 2.9 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> Lines are functions, even tangent lines.<br/> </div> </li> <li class="level1"><div class="li"> Linearization of a function f(x) approximates the values of f(x).<br/> </div> </li> <li class="level1"><div class="li"> The change along the y-axis can be approximated with linearization.</div> </li> </ul> </div><!-- EDIT15 PLUGIN_WRAP_END [0-] --><!-- EDIT16 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT18 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.9_linearization_differentials.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.9_linearization_differentials.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT19 PLUGIN_WRAP_END [0-] --><!-- EDIT20 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/2.9_linearization_differentials_tex.html" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/2.9_linearization_differentials_tex.html">Classroom Slides TEX</a> </p> </div><!-- EDIT21 PLUGIN_WRAP_END [0-] --></div><!-- EDIT17 PLUGIN_WRAP_END [0-] --></div><!-- EDIT13 PLUGIN_WRAP_END [0-] --></div><!-- EDIT2 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT22 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT24 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit26" id="critical_points_and_the_closed_interval_method">Critical Points and the Closed Interval Method</h2> <!-- EDIT26 SECTION "Critical Points and the Closed Interval Method" [2506-] --></div><!-- EDIT25 PLUGIN_WRAP_END [0-] --><!-- EDIT27 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT29 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/5ooKqwH3gvs" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT30 PLUGIN_WRAP_END [0-] --><!-- EDIT31 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/qIilPJYGwg4" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT32 PLUGIN_WRAP_END [0-] --></div><!-- EDIT28 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT33 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT35 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 3.1 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> Graphical understanding of extrema.<br/> </div> </li> <li class="level1"><div class="li"> Fermat&#039;s Theorem.<br/> </div> </li> <li class="level1"><div class="li"> Local extrema are critical points, the opposite isn&#039;t necessarily true.<br/> </div> </li> <li class="level1"><div class="li"> Extreme Value Theorem.<br/> </div> </li> <li class="level1"><div class="li"> The Closed Interval Method.</div> </li> </ul> </div><!-- EDIT36 PLUGIN_WRAP_END [0-] --><!-- EDIT37 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT39 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.1_critical_points.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.1_critical_points.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT40 PLUGIN_WRAP_END [0-] --><!-- EDIT41 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.1_critical_points_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.1_critical_points_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT42 PLUGIN_WRAP_END [0-] --></div><!-- EDIT38 PLUGIN_WRAP_END [0-] --></div><!-- EDIT34 PLUGIN_WRAP_END [0-] --></div><!-- EDIT23 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT43 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT45 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit47" id="the_mean_value_theorem">The Mean Value Theorem</h2> <!-- EDIT47 SECTION "The Mean Value Theorem" [3465-] --> <p> <em>Section 3.2 in Stewart&#039;s Calculus.</em> </p> </div><!-- EDIT46 PLUGIN_WRAP_END [0-] --><!-- EDIT48 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT50 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.2_mean_value_theorem.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.2_mean_value_theorem.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT51 PLUGIN_WRAP_END [0-] --><!-- EDIT52 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.2_mean_value_theorem_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.2_mean_value_theorem_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT53 PLUGIN_WRAP_END [0-] --></div><!-- EDIT49 PLUGIN_WRAP_END [0-] --></div><!-- EDIT44 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT54 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT56 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit58" id="the_shape_of_a_graph">The Shape of a Graph</h2> <!-- EDIT58 SECTION "The Shape of a Graph" [3990-] --></div><!-- EDIT57 PLUGIN_WRAP_END [0-] --><!-- EDIT59 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT61 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/npez7AKzCfM" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT62 PLUGIN_WRAP_END [0-] --><!-- EDIT63 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/IsQ6Zi-g51Q" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT64 PLUGIN_WRAP_END [0-] --></div><!-- EDIT60 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT65 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT67 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 3.3 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> If the derivative is positive on an interval, the original function is increasing on that interval. If the derivative is negative on an interval, the original function is decreasing on that interval.<br/> </div> </li> <li class="level1"><div class="li"> Concavity describes the direction a function is bending. A function is concave up on an interval, then the second derivative is positive on that interval and the function bends upwards. A function is concave down on an interval, the second derivative is negative on that interval and the function bends downwards.</div> </li> </ul> </div><!-- EDIT68 PLUGIN_WRAP_END [0-] --><!-- EDIT69 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT71 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.3_graph_shape.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.3_graph_shape.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT72 PLUGIN_WRAP_END [0-] --><!-- EDIT73 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.3_graph_shape_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.3_graph_shape_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT74 PLUGIN_WRAP_END [0-] --></div><!-- EDIT70 PLUGIN_WRAP_END [0-] --></div><!-- EDIT66 PLUGIN_WRAP_END [0-] --></div><!-- EDIT55 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT75 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT77 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit79" id="horizontal_asymptotes">Horizontal Asymptotes</h2> <!-- EDIT79 SECTION "Horizontal Asymptotes" [5230-] --></div><!-- EDIT78 PLUGIN_WRAP_END [0-] --><!-- EDIT80 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT82 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/E29ZLZ_EoCI" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT83 PLUGIN_WRAP_END [0-] --><!-- EDIT84 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/BoJbExhO5rI" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT85 PLUGIN_WRAP_END [0-] --></div><!-- EDIT81 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT86 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT88 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 3.4 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> The end behavior of a function is described with limits.<br/> </div> </li> <li class="level1"><div class="li"> Horizontal asymptotes of power functions are either zero or do not exist (tend towards infinity).<br/> </div> </li> <li class="level1"><div class="li"> Determinate and indeterminate forms.<br/> </div> </li> </ul> </div><!-- EDIT89 PLUGIN_WRAP_END [0-] --><!-- EDIT90 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT92 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.4_horizontal_asymptotes.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.4_horizontal_asymptotes.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT93 PLUGIN_WRAP_END [0-] --><!-- EDIT94 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.4_horizontal_asymptotes_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.4_horizontal_asymptotes_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT95 PLUGIN_WRAP_END [0-] --></div><!-- EDIT91 PLUGIN_WRAP_END [0-] --></div><!-- EDIT87 PLUGIN_WRAP_END [0-] --></div><!-- EDIT76 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT96 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT98 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit100" id="curve_sketching">Curve Sketching</h2> <!-- EDIT100 SECTION "Curve Sketching" [6179-] --></div><!-- EDIT99 PLUGIN_WRAP_END [0-] --><!-- EDIT101 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT103 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/hfkgjFf2vLU" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT104 PLUGIN_WRAP_END [0-] --><!-- EDIT105 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT107 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 3.5 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> The basics of curve sketching. </div> </li> </ul> </div><!-- EDIT108 PLUGIN_WRAP_END [0-] --></div><!-- EDIT106 PLUGIN_WRAP_END [0-] --></div><!-- EDIT102 PLUGIN_WRAP_END [0-] --></div><!-- EDIT97 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT109 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT111 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit113" id="optimization">Optimization</h2> <!-- EDIT113 SECTION "Optimization" [6497-] --></div><!-- EDIT112 PLUGIN_WRAP_END [0-] --><!-- EDIT114 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT116 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/U1t1dJbQtgg" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT117 PLUGIN_WRAP_END [0-] --><!-- EDIT118 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT120 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 3.7 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Optimized solutions to problems are found at critical points. This technique is useful in obtaining information in natural, less mathematical, settings.<br/> </div> </li> </ul> </div><!-- EDIT121 PLUGIN_WRAP_END [0-] --><!-- EDIT122 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT123 PLUGIN_WRAP_END [0-] --><!-- EDIT124 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.7_optimization.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.7_optimization.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT125 PLUGIN_WRAP_END [0-] --><!-- EDIT126 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT127 PLUGIN_WRAP_END [0-] --><!-- EDIT128 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.7_optimization_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.7_optimization_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT129 PLUGIN_WRAP_END [0-] --></div><!-- EDIT119 PLUGIN_WRAP_END [0-] --></div><!-- EDIT115 PLUGIN_WRAP_END [0-] --></div><!-- EDIT110 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT130 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT132 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit134" id="antiderivatives">Antiderivatives</h2> <!-- EDIT134 SECTION "Antiderivatives" [7315-] --></div><!-- EDIT133 PLUGIN_WRAP_END [0-] --><!-- EDIT135 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT137 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/tzjvqUO2kDM" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT138 PLUGIN_WRAP_END [0-] --><!-- EDIT139 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT141 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 3.9 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Antiderivatives of a function f(x) are functions whose derivative is f(x).<br/> </div> </li> <li class="level1"><div class="li"> The antiderivatives of a function differ by only a constant.<br/> </div> </li> <li class="level1"><div class="li"> Antiderivatives of common functions.<br/> </div> </li> </ul> </div><!-- EDIT142 PLUGIN_WRAP_END [0-] --><!-- EDIT143 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT144 PLUGIN_WRAP_END [0-] --><!-- EDIT145 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.9_antiderivatives.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.9_antiderivatives.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT146 PLUGIN_WRAP_END [0-] --><!-- EDIT147 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT148 PLUGIN_WRAP_END [0-] --><!-- EDIT149 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.9_antiderivatives_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.9_antiderivatives_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT150 PLUGIN_WRAP_END [0-] --></div><!-- EDIT140 PLUGIN_WRAP_END [0-] --></div><!-- EDIT136 PLUGIN_WRAP_END [0-] --></div><!-- EDIT131 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <p> <style> #footer { background-color:#006f3f; height: 16px; } #footer h1 { font-size: 14px; font-weight: bold; text-align: center; color: rgb(256,256,256); } </style> <div id="footer"><h1>Laura Anderson and Joseph Brennan</h1> </div> </p> Derivatives: Flipped Calculus at Binghamton SUNY 2015-08-28T22:35:37-04:00 2015-08-28T22:35:37-04:00 https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives <p> <style> #header { background-color:#006f3f; height: 55px; font-size: 21px; font-weight: bold; text-align: center; color: rgb(256,256,256) } #menu { height: 35px; font-size: 15px; font-family: Tahoma, Geneva, sans-serif; font-weight: bold; text-align: center; text-shadow: 3px 2px 3px #333333; background-color: rgb(102,156,156); } #menu ul { height: auto; padding: 8px 0px; margin: 0px; } #menu li { display: inline; padding: 16px; } #menu a { text-decoration: none; color: rgb(256,256,256); padding: 8px 8px 8px 8px; } #menu a:hover { color: #006f3f; background-color: #FFF; } </style> <div id="header"> <h1 style="margin-top:1; margin-bottom:1;">Flipped Calculus 1 at Binghamton</h1></div> <div id="menu"> <ul> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources">Home</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits">Limits</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives">Derivatives</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications">Applications</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals">Integrals</a></li> </ul> </div> <br/> </p> <!-- EDIT1 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT3 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit5" id="the_derivative_as_a_function">The Derivative as a Function</h2> <!-- EDIT5 SECTION "The Derivative as a Function" [1547-] --> <p> <br/> <em>Section 2.2 in Stewart&#039;s Calculus.</em> </p> </div><!-- EDIT4 PLUGIN_WRAP_END [0-] --><!-- EDIT6 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT8 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.2_derivative_function.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.2_derivative_function.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT9 PLUGIN_WRAP_END [0-] --><!-- EDIT10 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.2_derivative_function_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.2_derivative_function_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT11 PLUGIN_WRAP_END [0-] --></div><!-- EDIT7 PLUGIN_WRAP_END [0-] --></div><!-- EDIT2 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT12 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT14 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit16" id="differentiation_formulas">Differentiation Formulas</h2> <!-- EDIT16 SECTION "Differentiation Formulas" [2081-] --></div><!-- EDIT15 PLUGIN_WRAP_END [0-] --><!-- EDIT17 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT19 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/qFHSXnXSaS4" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT20 PLUGIN_WRAP_END [0-] --><!-- EDIT21 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT23 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 2.3 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Derivative formulas for powers and roots.<br/> </div> </li> <li class="level1"><div class="li"> Derivative formulas for sums/differences/products/quotients.</div> </li> </ul> </div><!-- EDIT24 PLUGIN_WRAP_END [0-] --><!-- EDIT25 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT26 PLUGIN_WRAP_END [0-] --><!-- EDIT27 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.3_differentiation_formulas.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.3_differentiation_formulas.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT28 PLUGIN_WRAP_END [0-] --><!-- EDIT29 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT30 PLUGIN_WRAP_END [0-] --><!-- EDIT31 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.3_differentiation_formulas_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.3_differentiation_formulas_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT32 PLUGIN_WRAP_END [0-] --></div><!-- EDIT22 PLUGIN_WRAP_END [0-] --></div><!-- EDIT18 PLUGIN_WRAP_END [0-] --></div><!-- EDIT13 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT33 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT35 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit37" id="trigonometric_derivatives">Trigonometric Derivatives</h2> <!-- EDIT37 SECTION "Trigonometric Derivatives" [2887-] --></div><!-- EDIT36 PLUGIN_WRAP_END [0-] --><!-- EDIT38 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT40 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/tafh4ANt-gs" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT41 PLUGIN_WRAP_END [0-] --><!-- EDIT42 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT44 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 2.4 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Familiarity with the limit of sin(x)/x as x approaches zero.</div> </li> </ul> </div><!-- EDIT45 PLUGIN_WRAP_END [0-] --><!-- EDIT46 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT47 PLUGIN_WRAP_END [0-] --><!-- EDIT48 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.4_trig_derivatives.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.4_trig_derivatives.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT49 PLUGIN_WRAP_END [0-] --><!-- EDIT50 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT51 PLUGIN_WRAP_END [0-] --><!-- EDIT52 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.4_trig_derivatives_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.4_trig_derivatives_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT53 PLUGIN_WRAP_END [0-] --></div><!-- EDIT43 PLUGIN_WRAP_END [0-] --></div><!-- EDIT39 PLUGIN_WRAP_END [0-] --></div><!-- EDIT34 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT54 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT56 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit58" id="the_chain_rule">The Chain Rule</h2> <!-- EDIT58 SECTION "The Chain Rule" [3629-] --></div><!-- EDIT57 PLUGIN_WRAP_END [0-] --><!-- EDIT59 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT61 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/bNwaBeNamr0" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT62 PLUGIN_WRAP_END [0-] --><!-- EDIT63 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT65 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 2.5 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Composition and rates of change.<br/> </div> </li> <li class="level1"><div class="li"> Chain Rule Formula.</div> </li> </ul> </div><!-- EDIT66 PLUGIN_WRAP_END [0-] --><!-- EDIT67 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT68 PLUGIN_WRAP_END [0-] --><!-- EDIT69 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.5_chain_rule.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.5_chain_rule.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT70 PLUGIN_WRAP_END [0-] --><!-- EDIT71 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT72 PLUGIN_WRAP_END [0-] --><!-- EDIT73 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.5_chain_rule_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.5_chain_rule_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT74 PLUGIN_WRAP_END [0-] --></div><!-- EDIT64 PLUGIN_WRAP_END [0-] --></div><!-- EDIT60 PLUGIN_WRAP_END [0-] --></div><!-- EDIT55 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT75 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT77 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit79" id="implicit_differentiation">Implicit Differentiation</h2> <!-- EDIT79 SECTION "Implicit Differentiation" [4347-] --></div><!-- EDIT78 PLUGIN_WRAP_END [0-] --><!-- EDIT80 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT82 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/LUtciqbWhyw" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT83 PLUGIN_WRAP_END [0-] --><!-- EDIT84 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/hUEDDP7CvPs" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT85 PLUGIN_WRAP_END [0-] --></div><!-- EDIT81 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT86 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT88 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 2.6 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> An equation implicitly defines many functions.<br/> </div> </li> <li class="level1"><div class="li"> Implicitly versus explicitly defined functions.<br/> </div> </li> <li class="level1"><div class="li"> Basics of Implicit Differntiation.</div> </li> </ul> </div><!-- EDIT89 PLUGIN_WRAP_END [0-] --><!-- EDIT90 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT92 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.6_implicit_differentiation.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.6_implicit_differentiation.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT93 PLUGIN_WRAP_END [0-] --><!-- EDIT94 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.6_implicit_differentiation_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.6_implicit_differentiation_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT95 PLUGIN_WRAP_END [0-] --></div><!-- EDIT91 PLUGIN_WRAP_END [0-] --></div><!-- EDIT87 PLUGIN_WRAP_END [0-] --></div><!-- EDIT76 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT96 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT98 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit100" id="rates_of_change_in_the_sciences">Rates of Change in the Sciences</h2> <!-- EDIT100 SECTION "Rates of Change in the Sciences" [5242-] --></div><!-- EDIT99 PLUGIN_WRAP_END [0-] --><!-- EDIT101 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT103 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/ZImKZBJlkRE" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT104 PLUGIN_WRAP_END [0-] --><!-- EDIT105 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT107 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 2.7 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Instantaneous Rates of Change are everywhere!</div> </li> </ul> </div><!-- EDIT108 PLUGIN_WRAP_END [0-] --><!-- EDIT109 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT110 PLUGIN_WRAP_END [0-] --><!-- EDIT111 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.7_sciences.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.7_sciences.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT112 PLUGIN_WRAP_END [0-] --><!-- EDIT113 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT114 PLUGIN_WRAP_END [0-] --><!-- EDIT115 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.7_sciences_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.7_sciences_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT116 PLUGIN_WRAP_END [0-] --></div><!-- EDIT106 PLUGIN_WRAP_END [0-] --></div><!-- EDIT102 PLUGIN_WRAP_END [0-] --></div><!-- EDIT97 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT117 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT119 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit121" id="related_rates">Related Rates</h2> <!-- EDIT121 SECTION "Related Rates" [5960-] --></div><!-- EDIT120 PLUGIN_WRAP_END [0-] --><!-- EDIT122 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT124 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/W6sPil54GQ8" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT125 PLUGIN_WRAP_END [0-] --><!-- EDIT126 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/Q0wgb9pYMoo" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT127 PLUGIN_WRAP_END [0-] --></div><!-- EDIT123 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT128 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT130 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 2.8 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> Rates of change can be found by implicitly differentiating an equation. This technique is useful in obtaining information in natural, less mathematical, settings.<br/> </div> </li> </ul> </div><!-- EDIT131 PLUGIN_WRAP_END [0-] --><!-- EDIT132 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT134 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.8_related_rates.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.8_related_rates.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT135 PLUGIN_WRAP_END [0-] --><!-- EDIT136 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.8_related_rates_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives/2.8_related_rates_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT137 PLUGIN_WRAP_END [0-] --></div><!-- EDIT133 PLUGIN_WRAP_END [0-] --></div><!-- EDIT129 PLUGIN_WRAP_END [0-] --></div><!-- EDIT118 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <p> <style> #footer { background-color:#006f3f; height: 16px; } #footer h1 { font-size: 14px; font-weight: bold; text-align: center; color: rgb(256,256,256); } </style> <div id="footer"><h1>Laura Anderson and Joseph Brennan</h1> </div> </p> Integrals: Flipped Calculus at Binghamton SUNY 2015-08-28T22:35:11-04:00 2015-08-28T22:35:11-04:00 https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals <p> <style> #header { background-color:#006f3f; height: 55px; font-size: 21px; font-weight: bold; text-align: center; color: rgb(256,256,256) } #menu { height: 35px; font-size: 15px; font-family: Tahoma, Geneva, sans-serif; font-weight: bold; text-align: center; text-shadow: 3px 2px 3px #333333; background-color: rgb(102,156,156); } #menu ul { height: auto; padding: 8px 0px; margin: 0px; } #menu li { display: inline; padding: 16px; } #menu a { text-decoration: none; color: rgb(256,256,256); padding: 8px 8px 8px 8px; } #menu a:hover { color: #006f3f; background-color: #FFF; } </style> <div id="header"> <h1 style="margin-top:1; margin-bottom:1;">Flipped Calculus 1 at Binghamton</h1></div> <div id="menu"> <ul> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources">Home</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits">Limits</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives">Derivatives</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications">Applications</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals">Integrals</a></li> </ul> </div> <br/> </p> <!-- EDIT1 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT3 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit5" id="definite_integrals">Definite Integrals</h2> <!-- EDIT5 SECTION "Definite Integrals" [1545-] --></div><!-- EDIT4 PLUGIN_WRAP_END [0-] --><!-- EDIT6 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT8 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/MivL_1A7Lxw" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT9 PLUGIN_WRAP_END [0-] --><!-- EDIT10 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/psKT74jZafs" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT11 PLUGIN_WRAP_END [0-] --></div><!-- EDIT7 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT12 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT14 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 4.2 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> Definite integrals calculate the area under a function over an interval.<br/> </div> </li> <li class="level1"><div class="li"> Riemann Sums.<br/> </div> </li> <li class="level1"><div class="li"> Properties of definite integrals.</div> </li> </ul> </div><!-- EDIT15 PLUGIN_WRAP_END [0-] --><!-- EDIT16 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT18 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.2_definite_integrals.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.2_definite_integrals.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT19 PLUGIN_WRAP_END [0-] --><!-- EDIT20 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals/4.2_definite_integrals_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals/4.2_definite_integrals_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT21 PLUGIN_WRAP_END [0-] --></div><!-- EDIT17 PLUGIN_WRAP_END [0-] --></div><!-- EDIT13 PLUGIN_WRAP_END [0-] --></div><!-- EDIT2 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT22 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT24 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit26" id="the_fundamental_theorem_of_calculus">The Fundamental Theorem of Calculus</h2> <!-- EDIT26 SECTION "The Fundamental Theorem of Calculus" [2408-] --> <p> <br/> <em>Section 4.3 in Stewart&#039;s Calculus.</em> </p> </div><!-- EDIT25 PLUGIN_WRAP_END [0-] --><!-- EDIT27 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT29 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.3_fundamental_theorem.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.3_fundamental_theorem.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT30 PLUGIN_WRAP_END [0-] --><!-- EDIT31 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.3_fundamental_theorem_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.3_fundamental_theorem_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT32 PLUGIN_WRAP_END [0-] --></div><!-- EDIT28 PLUGIN_WRAP_END [0-] --></div><!-- EDIT23 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT33 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT35 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit37" id="indefinite_integrals">Indefinite Integrals</h2> <!-- EDIT37 SECTION "Indefinite Integrals" [2949-] --></div><!-- EDIT36 PLUGIN_WRAP_END [0-] --><!-- EDIT38 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT40 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/z9nW0k5IQZo" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT41 PLUGIN_WRAP_END [0-] --><!-- EDIT42 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT44 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 4.4 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> An indefinite integral of a function is its general antiderivative. <br/> </div> </li> <li class="level1"><div class="li"> The definite integral of a rate of change is the net change.</div> </li> </ul> </div><!-- EDIT45 PLUGIN_WRAP_END [0-] --><!-- EDIT46 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT47 PLUGIN_WRAP_END [0-] --><!-- EDIT48 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.4_indefinite_integrals.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.4_indefinite_integrals.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT49 PLUGIN_WRAP_END [0-] --><!-- EDIT50 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT51 PLUGIN_WRAP_END [0-] --><!-- EDIT52 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.4_indefinite_integrals_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.4_indefinite_integrals_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT53 PLUGIN_WRAP_END [0-] --></div><!-- EDIT43 PLUGIN_WRAP_END [0-] --></div><!-- EDIT39 PLUGIN_WRAP_END [0-] --></div><!-- EDIT34 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT54 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT56 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit58" id="integration_with_substitution">Integration with Substitution</h2> <!-- EDIT58 SECTION "Integration with Substitution" [3771-] --></div><!-- EDIT57 PLUGIN_WRAP_END [0-] --><!-- EDIT59 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT61 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/4sCmHfBNpwM" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT62 PLUGIN_WRAP_END [0-] --><!-- EDIT63 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT65 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 4.5 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Substitution is the rule for integration which corresponds to the chain rule for differentiation.<br/> </div> </li> <li class="level1"><div class="li"> Introduction to integrating with substitution.</div> </li> </ul> </div><!-- EDIT66 PLUGIN_WRAP_END [0-] --><!-- EDIT67 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT68 PLUGIN_WRAP_END [0-] --><!-- EDIT69 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.5_substitution.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.5_substitution.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT70 PLUGIN_WRAP_END [0-] --><!-- EDIT71 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT72 PLUGIN_WRAP_END [0-] --><!-- EDIT73 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.5_substitution_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.5_substitution_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT74 PLUGIN_WRAP_END [0-] --></div><!-- EDIT64 PLUGIN_WRAP_END [0-] --></div><!-- EDIT60 PLUGIN_WRAP_END [0-] --></div><!-- EDIT55 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT75 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT77 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit79" id="area">Area</h2> <!-- EDIT79 SECTION "Area" [4601-] --></div><!-- EDIT78 PLUGIN_WRAP_END [0-] --><!-- EDIT80 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT82 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/g5MMts3tcHI" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT83 PLUGIN_WRAP_END [0-] --><!-- EDIT84 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT86 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 5.1 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Total area between functions f and g is calculated by integrating the absolute value of the difference of f and g. </div> </li> </ul> </div><!-- EDIT87 PLUGIN_WRAP_END [0-] --><!-- EDIT88 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT89 PLUGIN_WRAP_END [0-] --><!-- EDIT90 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.1_area.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.1_area.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT91 PLUGIN_WRAP_END [0-] --><!-- EDIT92 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT93 PLUGIN_WRAP_END [0-] --><!-- EDIT94 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.1_area_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.1_area_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT95 PLUGIN_WRAP_END [0-] --></div><!-- EDIT85 PLUGIN_WRAP_END [0-] --></div><!-- EDIT81 PLUGIN_WRAP_END [0-] --></div><!-- EDIT76 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT96 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT98 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit100" id="volume">Volume</h2> <!-- EDIT100 SECTION "Volume" [5354-] --></div><!-- EDIT99 PLUGIN_WRAP_END [0-] --><!-- EDIT101 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT103 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/FMU8PLT_CSg" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT104 PLUGIN_WRAP_END [0-] --><!-- EDIT105 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT107 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 5.2/5.3 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Formula for calculating volume using cylindrical shells.<br/> </div> </li> <li class="level1"><div class="li"> Differences between the washer and shell methods.</div> </li> </ul> </div><!-- EDIT108 PLUGIN_WRAP_END [0-] --><!-- EDIT109 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT110 PLUGIN_WRAP_END [0-] --><!-- EDIT111 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.3_cylindrical_shells.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.3_cylindrical_shells.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT112 PLUGIN_WRAP_END [0-] --><!-- EDIT113 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT114 PLUGIN_WRAP_END [0-] --><!-- EDIT115 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.3_cylindrical_shells_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.3_cylindrical_shells_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT116 PLUGIN_WRAP_END [0-] --></div><!-- EDIT106 PLUGIN_WRAP_END [0-] --></div><!-- EDIT102 PLUGIN_WRAP_END [0-] --></div><!-- EDIT97 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT117 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT119 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit121" id="the_average_value_of_a_function">The Average Value of a Function</h2> <!-- EDIT121 SECTION "The Average Value of a Function" [6139-] --></div><!-- EDIT120 PLUGIN_WRAP_END [0-] --><!-- EDIT122 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT124 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/IIkXga3YMik" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT125 PLUGIN_WRAP_END [0-] --><!-- EDIT126 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT128 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 5.5 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> Average Value Formula.</div> </li> </ul> </div><!-- EDIT129 PLUGIN_WRAP_END [0-] --><!-- EDIT130 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT131 PLUGIN_WRAP_END [0-] --><!-- EDIT132 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.5_average.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.5_average.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT133 PLUGIN_WRAP_END [0-] --><!-- EDIT134 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT135 PLUGIN_WRAP_END [0-] --><!-- EDIT136 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.5_average_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.5_average_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT137 PLUGIN_WRAP_END [0-] --></div><!-- EDIT127 PLUGIN_WRAP_END [0-] --></div><!-- EDIT123 PLUGIN_WRAP_END [0-] --></div><!-- EDIT118 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <p> <style> #footer { background-color:#006f3f; height: 16px; } #footer h1 { font-size: 14px; font-weight: bold; text-align: center; color: rgb(256,256,256); } </style> <div id="footer"><h1>Laura Anderson and Joseph Brennan</h1> </div> </p> Limits: Flipped Calculus at Binghamton SUNY 2015-08-28T22:35:33-04:00 2015-08-28T22:35:33-04:00 https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits <p> <style> #header { background-color:#006f3f; height: 55px; font-size: 21px; font-weight: bold; text-align: center; color: rgb(256,256,256) } #menu { height: 35px; font-size: 15px; font-family: Tahoma, Geneva, sans-serif; font-weight: bold; text-align: center; text-shadow: 3px 2px 3px #333333; background-color: rgb(102,156,156); } #menu ul { height: auto; padding: 8px 0px; margin: 0px; } #menu li { display: inline; padding: 16px; } #menu a { text-decoration: none; color: rgb(256,256,256); padding: 8px 8px 8px 8px; } #menu a:hover { color: #006f3f; background-color: #FFF; } </style> <div id="header"> <h1 style="margin-top:1; margin-bottom:1;">Flipped Calculus 1 at Binghamton</h1></div> <div id="menu"> <ul> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources">Home</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits">Limits</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives">Derivatives</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications">Applications</a></li> <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals">Integrals</a></li> </ul> </div> <br/> </p> <!-- EDIT1 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT3 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit5" id="the_limit_of_a_function">The Limit of a Function</h2> <!-- EDIT5 SECTION "The Limit of a Function" [1542-] --></div><!-- EDIT4 PLUGIN_WRAP_END [0-] --><!-- EDIT6 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT8 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/vaZfqpWYDO8" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT9 PLUGIN_WRAP_END [0-] --><!-- EDIT10 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT12 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 1.5 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em> <br/> </p> <ul> <li class="level1"><div class="li"> The limit at an x-value describes the y-value the function “approaches” at that x-value.<br/> </div> </li> <li class="level1"><div class="li"> Graphical intuition for limits.<br/> </div> </li> <li class="level1"><div class="li"> Two-sided limits depend on both one-sided limits.</div> </li> </ul> </div><!-- EDIT13 PLUGIN_WRAP_END [0-] --><!-- EDIT14 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT15 PLUGIN_WRAP_END [0-] --><!-- EDIT16 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.5_limit.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.5_limit.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT17 PLUGIN_WRAP_END [0-] --><!-- EDIT18 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT19 PLUGIN_WRAP_END [0-] --><!-- EDIT20 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.5_limit_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.5_limit_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT21 PLUGIN_WRAP_END [0-] --></div><!-- EDIT11 PLUGIN_WRAP_END [0-] --></div><!-- EDIT7 PLUGIN_WRAP_END [0-] --></div><!-- EDIT2 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT22 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT24 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit26" id="tangents_derivatives_and_rates_of_change">Tangents, Derivatives, and Rates of Change</h2> <!-- EDIT26 SECTION "Tangents, Derivatives, and Rates of Change" [2380-] --></div><!-- EDIT25 PLUGIN_WRAP_END [0-] --><!-- EDIT27 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT29 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/oqBLj4coFvg" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT30 PLUGIN_WRAP_END [0-] --><!-- EDIT31 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/9_3l1bqV4Ak" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT32 PLUGIN_WRAP_END [0-] --></div><!-- EDIT28 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT33 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT35 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 1.4/2.1 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> A rate of change describes how one quantity changes in relation to another quantity.<br/> </div> </li> <li class="level1"><div class="li"> Rate of change can result from averaging over an interval or finding a limit of averages approaching a single point.<br/> </div> </li> <li class="level1"><div class="li"> Tangent lines result from the limit of secant lines.<br/> </div> </li> <li class="level1"><div class="li"> A derivative is an instantaneous rate of change.</div> </li> </ul> </div><!-- EDIT36 PLUGIN_WRAP_END [0-] --></div><!-- EDIT34 PLUGIN_WRAP_END [0-] --><!-- EDIT37 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT39 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.4-2.1_rates_of_change.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.4-2.1_rates_of_change.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT40 PLUGIN_WRAP_END [0-] --><!-- EDIT41 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.4-2.1_rates_of_change_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.4-2.1_rates_of_change_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT42 PLUGIN_WRAP_END [0-] --></div><!-- EDIT38 PLUGIN_WRAP_END [0-] --></div><!-- EDIT23 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT43 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT45 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit47" id="limit_laws">Limit Laws</h2> <!-- EDIT47 SECTION "Limit Laws" [3462-] --></div><!-- EDIT46 PLUGIN_WRAP_END [0-] --><!-- EDIT48 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT50 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/jeiF2tm4Wx4" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT51 PLUGIN_WRAP_END [0-] --><!-- EDIT52 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/7RZJSTJQL5E" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT53 PLUGIN_WRAP_END [0-] --></div><!-- EDIT49 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT54 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT56 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 1.6 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> Algebraic limit laws.<br/> </div> </li> <li class="level1"><div class="li"> When direct substitution isn&#039;t allowable in calculating a limit try simplification, conjugation, or squeezing the function.</div> </li> </ul> </div><!-- EDIT57 PLUGIN_WRAP_END [0-] --><!-- EDIT58 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT60 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.6_limit_laws.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.6_limit_laws.pdf">Classroom Slides PDF</a> </p> </div><!-- EDIT61 PLUGIN_WRAP_END [0-] --><!-- EDIT62 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column wrap_centeralign plugin_wrap"> <p> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.6_limit_laws_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.6_limit_laws_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT63 PLUGIN_WRAP_END [0-] --></div><!-- EDIT59 PLUGIN_WRAP_END [0-] --></div><!-- EDIT55 PLUGIN_WRAP_END [0-] --></div><!-- EDIT44 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT64 PLUGIN_WRAP_START [0-] --><div class="wrap_box plugin_wrap" style="width:750px;"><!-- EDIT66 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <h2 class="sectionedit68" id="continuity">Continuity</h2> <!-- EDIT68 SECTION "Continuity" [4317-] --></div><!-- EDIT67 PLUGIN_WRAP_END [0-] --><!-- EDIT69 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT71 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/h836P0BCEcI" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT72 PLUGIN_WRAP_END [0-] --><!-- EDIT73 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/sb13L83w0n0" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT74 PLUGIN_WRAP_END [0-] --></div><!-- EDIT70 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <!-- EDIT75 PLUGIN_WRAP_START [0-] --><div class="wrap_group plugin_wrap"><!-- EDIT77 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><iframe src="https://www.youtube.com/embed/75Q69ZyOz5c" height="350" width="425" class="vshare__none" allowfullscreen="" frameborder="0" scrolling="no"></iframe></div><!-- EDIT78 PLUGIN_WRAP_END [0-] --><!-- EDIT79 PLUGIN_WRAP_START [0-] --><div class="wrap_half wrap_column plugin_wrap"><!-- EDIT81 PLUGIN_WRAP_START [0-] --><div class="plugin_wrap"> <p> <em>Section 1.8 in Stewart&#039;s Calculus.</em><br/> <br/> <em class="u"><strong>Preclass Learning Objectives:</strong></em><br/> </p> <ul> <li class="level1"><div class="li"> Graphical intuition of continuity.<br/> </div> </li> <li class="level1"><div class="li"> Where limits align with actual values, a function is continuous.<br/> </div> </li> <li class="level1"><div class="li"> Types of discontinuities.<br/> </div> </li> <li class="level1"><div class="li"> Algebraic limit laws.<br/> </div> </li> <li class="level1"><div class="li"> Continuous functions cannot jump (Intermediate Value Theorem).</div> </li> </ul> </div><!-- EDIT82 PLUGIN_WRAP_END [0-] --><!-- EDIT83 PLUGIN_WRAP_START [0-] --><div class="wrap_clear plugin_wrap"></div><!-- EDIT84 PLUGIN_WRAP_END [0-] --><!-- EDIT85 PLUGIN_WRAP_START [0-] --><div class="wrap_centeralign plugin_wrap"> <p> <a href="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.8_continuity.pdf" class="urlextern" title="http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.8_continuity.pdf">Classroom Slides PDF</a><br/> <br/> <a href="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.8_continuity_tex" class="urlextern" title="https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.8_continuity_tex">Classroom Slides TEX</a> </p> </div><!-- EDIT86 PLUGIN_WRAP_END [0-] --></div><!-- EDIT80 PLUGIN_WRAP_END [0-] --></div><!-- EDIT76 PLUGIN_WRAP_END [0-] --></div><!-- EDIT65 PLUGIN_WRAP_END [0-] --> <p> <br/> </p> <p> <style> #footer { background-color:#006f3f; height: 16px; } #footer h1 { font-size: 14px; font-weight: bold; text-align: center; color: rgb(256,256,256); } </style> <div id="footer"><h1>Laura Anderson and Joseph Brennan</h1> </div> </p>