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Tuesday, March 24, 2009

"Where My Little Bird Gets Caught In The Wind." - D. Kuropatwa.

I just kept hearing that quote for some reason, everytime the class would talk about the images of a slope field, since it sort of looks like a flock of geese flying in a certain direction.

I'm running out of creative titles, and my head is going in circles... BUT... let's get straight to it. I didn't scribe the other day, since we didn't have class. It's only fair, right?

As usual, we started off AP class breaking the ice...well that's not quite the ... correct term. We had a little chit chat session and in the middle of that, I told Mr. K, and judging by my natural loudness the whole class about my feelings about where my presence will be during Thursday's class. I was asking for his opinion, and I gave him the power of deciding for me, but we moved on to the lesson. Or... just another current topic in calculus.

Another PRE PRE LESSON... I am not making sense tonight. :S Anyhow, before we began the day's lesson, Mr. K showed the class the presentation and conference that was done yesterday afternoon with the lovely teachers in Saskatchewan. I thought it was extremely great how technology could be integrated with everything, which was the whole ball of wax about it. The conference was about how we mix education and technology, giving it a little FLAIR. [spelling?] :D

**NOTE, mentioned during the presentation were new forms of online communication, and possible DEV working methods, between members in a group!

GEOCACHING: a way of communicating being in the same space, but during different times.

DIMDIM: is a website,, in which a person can set up conferences to collaborate with group members without being in the same place. It's basically the opposite idea of GEOCACHING; meaning that people are communicating at the same time, but in different spaces.



The class started off by posting up the answers to our previous homework, reflecting on what we learned about slope fields so far.

For example, without being too mechanic, I'll explain...well, the mechanics of the second slope field, where, dy/dx = 2x.

The notation dy/dx shows that the equation is a derivative, and fits into the definition of a differential equation, where one variable is a derivative. 2x is an x dependent function, ergo, an x dependent derivative.

Then, we look at certain points on the axes, and determine what the slopes would be at that point. It is similar to plotting points on a graph, but instead using slopes within certain regions inside each quadrant. Once the grid is finally filled up with a variation of slopes, a "picture" is sort of painted.

The slope field takes the shape of a parabola. Now, mathematically, we know that 2x is the derivative of x2. But what always seems to be forgotten when anti-differentiating a function is always the idea of "+ C" at the end. This represents that A FAMILY of FUNCTIONS can be differentiated and still get 2x as the rate of change. The slope field depicts the family of possible parent functions.

Immediately after, we were given possible multiple choice questions that might make an appearance on the exam. These are shown on slides 4, 5, 8 and 9. Slide 9 is our homework, I believe, along with exercise 9.2.

The rest of the slides are pretty straight forward, with an exception of slide 5, and slide 8.
The only thing to be noted here, wasn't really because it was difficult, but it was worth noting. There was a specific pattern in this slope field, where the slopes are the same for a period, going in a constant direction, and all of the other slopes appear to be "bouncing" off of that "line" of slopes, then that line that slopes are bouncing off of is an asymptote. That was a really bad explanation. I can't quite articulate it correctly, but it's at the tip of my tongue.

As for slide 8...

This was one of those times when we got the correct answer, but we couldn't exactly explain how we got that specific answer, well not thoroughly at least. We mechanically knew what we were supposed to do, but the thought of how it works and WHY it works slipped our minds. Then it was time for. CALC. SCENE. INVESTIGATION.

Mathematically, the majority of the class massaged the equation by "finding the limit", making the denominator equal to ZERO. But WHY?!

REASON: Vertical segments are where the slopes of a tangent line, [derivative] are undefined and are therefore vertical, since a number is being divided by ZERO. That's the big whoop that we couldn't really fit together in class this morning. Once again, I'm sorry that my explanations are probably not up to par, but I am.. KABLUWEEE today. Nerves are kicking in, and my eyes are bloodshot. Too many things going on. I really don't like that this post is bland and what I don't like more is that I don't have much energy to read this over again and change it.


As for the tradition that the class has recently started, I'm just going to embed and shamelessly advertise videos from youtube on this post. BECAUSE all I have to do is COPY and PASTE. The two most powerful commands a computer person could ever know.


I'm abusing this and posting 1, since they aren't necessarily FUNNY. It's just something that I'd like to learn. IN THE NEAR FUTURE. I just thought it was necessary to show the world what they're missing. :D

FIRST OFF. MEET SHAUNA NOLAND. Incredible flexibility. I call her ALIEN.

About 0:10 - 0:14 s. in this video. I've tried this, and have fallen with a loud THUMP each time. And sorry for the bad TV synch, it was the only embeddable one.

THIS ONE... TUTTING is an art form which I make look like doggy doo. Kristina will probably enjoy the chopsticks skills at the end. You know I conquer. LULZ.

Lastly, Francis, you're the next scribe.


kristina said...

I was expecting him to pick up that lollipop with those chopsticks... baaw :(

.:. J + ME .:. said...

I thought you were asleep. This was supposed to be a morning surprise. LOL. well I'm off to bed. I'm caught too I guess. Better rest for the big day tomorrow :S