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<title>
Day 15 Tues
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<h2>Day 15 topics</h2>
<p class="show">Sections  13.4, 13.6-8
<ul>
<li>Two forms of Green's Theorem:
$$\oint_C P\,dx+Q\,dy=\iint_D\left(\frac{\del Q}{\del x} - \frac{\del P}{\del dy}\right)dA$$
$$\oint_C -Q\,dx+P\,dy=\iint_D\left(\frac{\del P}{\del x} + \frac{\del Q}{\del  y}\right)dA$$
<li>The extension of Green's Theorem to domains with holes. (Not covered in class).

<li>The practical importance of Green's Theorem: To replace a difficult line integral with an easier area integral - or to replace a difficult area integral with an easier line integral. 

<li>The idea of a surface integral of a scalar function  as an extension of the surface area integral.

<li>The idea of an oriented surface and positive orientation.
<li>The surface integral of a vector field over an oriented surface.
<li>The statement of Stokes theorem.
<li>The connection between curl and circulation.
<li>The meaning of a simple closed solid region R and its boundary surface .
<li>A careful statement of the Divergence Theorem 
</ul>



<h4 class="show"><a href="../handouts/Class15/">Class 15 Resources</a></h4>



<h4 class="show" id="tomorrow">To do for Wednesday</h4>
<ul>
  <li>WebAssign HW 15
  <li>WebAssign Test 3 quiz
</ul>
