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<h2 class="hd hd-2 unit-title">1. Syllabus and Schedule</h2>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Getting started</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 6 November</h4>
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<td style="text-align: left;" rowspan="6"><span style="color: #27408c;"><b class="bf">Overview and logistics</b></span></td>
<td style="text-align: left;">Meet the course team</td>
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<td style="text-align: left;">Course description</td>
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<td style="text-align: left;">Prerequisites and resources</td>
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<td style="text-align: left;">Syllabus</td>
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<td style="text-align: left;">Grading </td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Tutorial on using the edX platform</b></span></td>
<td style="text-align: left;">Navigating courseware</td>
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<td style="text-align: left;">Interactive problems</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Getting to know you</b></span></td>
<td style="text-align: left;">Diagnostics</td>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 1: The integral</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 6 November</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 4 December</h4>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Mean Value Theorem</b></span></td>
<td style="text-align: left;">Conclusion and Hypotheses of the Mean Value Theorem</td>
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<td style="text-align: left;">Using bounds on the derivative to gain bounds on the average value</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Differentials and Antiderivatives</b></span></td>
<td style="text-align: left;">Differentials and linear approximations</td>
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<td style="text-align: left;">Antiderivatives and the indefinite integral</td>
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<td style="text-align: left;">Method of substitution</td>
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<td style="text-align: left;" rowspan="5"><span style="color: #27408c;"><b class="bf">Differential Equations</b></span></td>
<td style="text-align: left;">Separation of variables</td>
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<td style="text-align: left;">Solutions to differential equations are infinite families of functions</td>
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<td style="text-align: left;">Solving differential equations with initial conditions</td>
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<td style="text-align: left;">Slope fields and solution curves</td>
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<td style="text-align: left;">Euler's method</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Modeling a Zipline</b></span></td>
<td style="text-align: left;">Hyperbolic sine and hyperbolic cosine</td>
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<td style="text-align: left;">Modeling a hanging cable with a differential equation</td>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 2: Integration Theory</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 6 November</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 8 January</h4>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Definite Integral</b></span></td>
<td style="text-align: left;">Reimann Sums</td>
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<td style="text-align: left;">Definite integral as the area under a curve</td>
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<td style="text-align: left;" rowspan="5"><span style="color: #27408c;"><b class="bf">Fundamental Theorem of Calculus</b></span></td>
<td style="text-align: left;">Connection between indefinite and definite integrals</td>
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<td style="text-align: left;">Signed areas under curves</td>
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<td style="text-align: left;">Properties of definite integrals</td>
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<td style="text-align: left;">Substitution for definite integrals</td>
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<td style="text-align: left;">Comparison of MVT and FTC1</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Second Fundamental Theorem of Calculus</b></span></td>
<td style="text-align: left;">Proof of FTC1</td>
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<td style="text-align: left;">Proof of FTC2</td>
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<td style="text-align: left;">Functions defined by definite integrals</td>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 3: Applications</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 6 November</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 29 January</h4>
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<td style="text-align: left;" rowspan="4"><span style="color: #27408c;"><b class="bf">Areas and Volumes</b></span></td>
<td style="text-align: left;">Areas between curves</td>
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<td style="text-align: left;">Volumes of revolution</td>
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<td style="text-align: left;">Computing Volumes: Method of Disks and Washers</td>
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<td style="text-align: left;">Computing Volumes: Method of Shells</td>
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<td style="text-align: left;" rowspan="4"><span style="color: #27408c;"><b class="bf">Average Value</b></span></td>
<td style="text-align: left;">Average value of continuous functions</td>
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<td style="text-align: left;">Weighted averages</td>
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<td style="text-align: left;">Center of mass</td>
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<td style="text-align: left;">Work</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Probability</b></span></td>
<td style="text-align: left;">Probability as a weighted average</td>
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<td style="text-align: left;">Setting up and solving probability problems</td>
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<td style="text-align: left;">The normal distribution and its integral</td>
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<td style="text-align: left;" rowspan="4"><span style="color: #27408c;"><b class="bf">Numerical Integration</b></span></td>
<td style="text-align: left;">Right and Left Riemmann sums</td>
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<td style="text-align: left;">Trapezoid rule</td>
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<td style="text-align: left;">Simpson's rule</td>
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<td style="text-align: left;">Functions whose integrals have no analytic solution</td>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 4: Techniques of Integration</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 6 November</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 19 February</h4>
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<td style="text-align: left;" rowspan="1"><span style="color: #27408c;"><b class="bf">Trigonometric powers</b></span></td>
<td style="text-align: left;">Integrating powers of trig functions</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Trigonometric substitution</b></span></td>
<td style="text-align: left;">Using appropriate trig substitution</td>
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<td style="text-align: left;">Evaluating inverse trig functions</td>
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<td style="text-align: left;">Completing the square</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Partial fractions</b></span></td>
<td style="text-align: left;">Integrating rational functions</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Integration by parts</b></span></td>
<td style="text-align: left;">Integration by parts</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Arc length and surface area</b></span></td>
<td style="text-align: left;">Computing arc length of curves</td>
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<td style="text-align: left;">Computing surface areas of surfaces of revolution</td>
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