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<title>
Day 14 Mon
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<h2>Day 14 topics</h2>
<p class="show">Sections  13.2-13.4
<ul>
   <li>The meaning of the line integral of a function $f$  along a curve $C$.
  <li>The meaning of $\int_C\left(P\,dx + Q\,dy\right)$ along a curve $C$.
<li>The meaning of $\int_C \myv F\cdot d\myv r$ – Vector fields and Work.
  <li>The path independence of $\int_C\myv \grad f\cdot d\myv r = \myv r(b)-\myv r(a)$ under suitable conditions.
  <li>Path independence is equivalent to the condition that $\oint_C \myv F\cdot d\myv r=0$  for every closed curve $C$ in the domain of $F$.

  <li>The equivalence of the following three statements on a simply connected domain:<ul>
  <li>Path independence.
  <li>$\myv F = M\uv i + N\uv j$ is a conservative vector field.  That is, $\myv F=\myv \grad f$ 
for some function f.
  <li>$\frac{\del M}{\del y}=\frac{\del N}{\del x}$.
</ul>


</ul>

<h4 class="show"><a href="../handouts/Class14/">Class 14 Resources</a></h4>



<h4 class="show" id="tomorrow">To do for Tuesday</h4>
<ul>
  <li>Read sections 13.4, 13.6-8
  <li>Answer the reading questions for Class 15
  <li>Complete all Class 14 worksheets / HW
  <li>WebAssign HW 14
</ul>





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