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<title>
VECTOR CALCULUS: Vector Fields [13.1]
</title>
<meta name="week" content="13">
<!--meta name="nolink" content="nolink"-->
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<h1>
Vector fields
</h1>
<p class="show"><img src="/physix/213/_g/pidgy.jpg">


<h3>2D vector field</h3>
<p class="show"><img src="0g/13.1.def1.jpg"><br>
<img src="0g/13.1.arrows.jpg">


<h3>2D vector field</h3>
<p class="show"><img src="0g/13.1.def2.jpg"><br>
<img src="0g/13.1.arrows3d.jpg">


<h3>To do</h3>
<ul class="else"><li>Vector Fields (Sketching)
</ul>

<h3>Examples</h3>
<p class="show"><img src="0g/13.1.vf1.jpg">

<h3>Examples</h3>
<p class="show"><img src="0g/13.1.vf2.jpg">

<h3>Examples</h3>
<p class="show"><img src="0g/13.1.vf3.jpg">

<h3>Examples</h3>
<p class="show"><img src="0g/13.1.vf4.jpg">

<h3>Examples</h3>
<p class="show">$$\myv F(x,y)=-y\uv i +x \uv j$$
<br><img src="0g/13.1.vf5.jpg">

<h3>Examples</h3>
<p class="show">$$\myv F(x,y,z)=z\uv k$$
<br><img src="0g/13.1.vf6.jpg">



<h3>Mathematica</h3>
<p class="show"><a href="/physix/213/handouts/VectorFields.nb">Example notebook</a> in today's resource folder.
<ul><li><tt>VectorPlot</tt> - 2D vector fields<br>
$$\myv F(x,y)=y\uv i -x\uv j$$<br>
<img src="0g/13.1.mtica1.jpg"><br>

<li><tt>VectorPlot3D</tt> - 3D vector fields<br>
$$\myv F(x,y)=y\uv i+z\uv j+x\uv k$$
<img src="0g/13.1.mtica2.jpg"><br>
</ul>


<p><img src="0g/13.1.scalem1.jpg" class="big"><br>
Use  <tt>VectorScale $\to$ Automatic</tt> if necessary
<p>
<img src="0g/13.1.scaleagain.jpg" class="big"><br>

<h3>To Do</h3>
<p class="show">Sketch these in Mathematica:
<ul class="else">
<li>$\myv F(x,y)=x^2 \uv i +x^3 \uv j$
<li>$\myv F(x,y)=y^3 \uv i +y^2 \uv j
$
<li>$\myv F(x,y)=(x+y) \uv i +(x-y) \uv j$
</ul>

<h3>To Do</h3>
<p class="show">Sketch these in Mathematica:
<ul class="else">
<li>$\myv F(x,y,z)=y \uv i + z \uv j + x \uv k$
<li>$\myv F(x,y,z)=y\uv i -2 \uv j +x \uv k$
<li>$\myv F(x,y,z)=1\uv i -y^2 \uv j +z\uv k$
</ul>
<h3>Example</h3>
<p class="show"><img src="0g/13.1.ex3d.jpg">










<h4 class="handout">Image credits</h4>
<p class="handout"><a href=""></a>

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