So, Firefox just crashed and deleted my whole scribe post when I had one word left. Fun night. We started off class with a brief discussion of the midterm and how it is going to work. Basically, it will include non-calc and calc free-response questions so be prepared for both. Also, homework is due Friday, except for today's assignment which is due Wednesday, which is also the day we have a quiz on Diffy Qs.
In class today, we began by talking about #6 on the slope fields packet. We also talked about the hot tub word problem. Here are a few helpful hints to keep in mind when working on Diffy Q problems:
-If you have a hard time with slope fields, make a table of values!
-You only need to add "C" to one side of your anti-derivative equation, as if you add c to both sides then subtract from one side, you still have a constant.
-Just because you are taking the anti-derivative of a fraction doesn't mean the anti-derivative is necessarily the natural log function
We then talked about Julia moving around the room. This taught us about position, displacement, and distance. We learned that position was Julia's location at a particular moment (e.g. position was -8 when Julia was at -8). Displacement was how far Julia traveled from her start location to her ending location, or final position minus initial position (e.g. Julia started at -8 and ended at -1 so her displacement was 7). We then decided that distance is how far Julia traveled total, and it must always be positive, as you can't un-travel. Julia's distance was 13, as it was the total of the absolute value of each leg of her trip (she started at -8, went to 2, then went back to -1). We then had a little discussion about how her velocity related to her movements. For example, as Julia went from -8 to 2, her velocity was positive, and was increasing then decreasing. As Julia traveled from 2 to -1, her velocity was negative, and was decreasing then increasing. The homework packet has a nice fill-in-the-blank section that explains this a little better, and Mr. O'Brien says that the concept of velocity in relation to displacement and distance can be a little hard to grasp at first. Overall, it was a productive class!
Here are a few links to help with today's lesson:
http://www.schooltube.com/video/4eae3449edc2899b3d00/Calculating-the-distance-between-two-points-on-a-number-line-by-Camille-Morton She makes understanding distances easy enough for a five-year-old to understand. It's cheesy, so be warned.
http://www.intmath.com/Differential-equations/1_Solving-DEs.php This breaks down differential equations into a manageable form, which I found helpful before the quiz Wednesday.
Homework: Packet Mr. O'Brien handed out, quiz on differential equations Wednesday, extra credit to anyone who can find a good visual representation of #6 in the slope fields packet.
UPDATE:
While looking for some practice problems for the midterm, I came across this link:
http://www.analyzemath.com/calculus.html
It has a bunch of problems for quite a few of the topics we've done so far and applets to help explain them!
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