Scribe Post 1/4/13

     We started our first full class of 2013 with a super-correction follow up test.  After 40 minutes of showing off our knowledge of derivatives and optimization we moved on to a new and very scary subject:

THE SLOPE FIELD

     Yeah, I know, it looks really hard, but it is actually really simple! This particular slope field is of the equation .  In order to make the slope field from this equation you simply start plugging in points! For this particular example we will start with the point (1,1).  Plug this into the equation so =-1.  This means that the slope at (1,1) is -1.  How does this relate to our slope field?

 Put a short line segment at (1,1) with a slope of -1.  During class there was some confusion on how long to make the segment.  It actually doesn't matter how long you make your segments.  Just make them a length that looks good!

     So you have one slope, continue plugging in points, keep plugging them in until you have a good idea of what will happen as far as slope.  In slope field problems you will be given a point such as (3,3) at which you need to evaluate your slope field.  You can then find the slope at that point and follow where it is pointing.  Keep following the slopes until you have a line!

     If you did this on the slope field above you would have a circle!

 If you want to make a slope field on Geogebra look at this website. I didn't try, but you're welcome to: https://prep11geogebra.pbworks.com/w/page/37697579/SlopeFieldsGeoGebra4

     

    Now O'Brien gave us a preview of a future lesson: how to solve a differential equation algebraically.

  

Up to the last step everything should make sense. Those squiggle things mean take the antiderivative.

As O'Brien said, this is not something to be freaking out about right now because we are just looking ahead. 

When you solve the equation you end up with an intercept (c) of 9

So, using the equation for a circle we find that 

and the radius is the square root of 18.

Okay, now that everybody is thoroughly confused lets have a recap of the fun game we played!

After an intense competition the medal platform had Gabe and Eben at the top with a gold, the dream team of JOC and #Calrobbins came in a close second, taking the silver and in a moment of pure euphoria Conor Hart celebrated his tie for the bronze with his teammate Claire, they tied Duncan and Eddie in third.

Next scribe? possibly you!