wordsworth

So for these videos there are two separate teachers. The first 50 minute video is taught by the professor and the videos about the general rules for differentiation are taught by a substitute. The information taught by the teacher seemed pretty complex. He is trying to prove the parts of a previous equation involving sin and cos. In order to do this he must some a geometric proof, which pretty obviously involves drawing a picture. Sine and Cosine are usually represented with a unit circle, which means that theta – a greek letter that relates to angles. A circle is 2theta or 360 degrees. The first step in these proofs is to replace delta x with theta. Pretty straight forward… maybe. It is kinda hard to describe in words but basically you draw a circle with an angle created that ends in the center. The arc within the angle is the arc-length-theta. The vertical length of the angle, the line that would make a triangular shape within the pie shaped angle, is what sin(theta) measures.  So basically in class the teacher made a bow and arrow on the board. The equations is (2sin(theta)/2theta), where 2sin(theta) is the bow string and 2theta is the bow. This equation equals 1 when theta goes to zero. As theta gets smaller the bow part looks almost straight and the string and bow would merge to become one. As the teacher said “short pieces of curves are nearly straight.” There were a bunch of other proof part like this one, usually involving circles and thetas. Some were pretty easy to understand, and basically straight forward, others were more confusing.

So this video was pretty interesting. The professor stopped class what seemed half way through, I guess that class was over. Then during the next class there was a substitute teacher. On the video you could hear the rumblings of the students. That is what happens when there is a substitute. The class gets all rumbly, every time. Anyway we talked about the Rules for Derivatives. He went back over what the teacher did, but only slightly. These rules have to do with the general derivative equations. These do not confuse me as must because they are straight forward formulas. You look at the problem and if it looks a certain way then you set it up in a corresponding fashion. For example if you have a problem in the form (uv)’ ( the ‘ means it is the derivative of the functions within the parenthesis) equals u’v+uv’. Therefore you must know the derivatives of both of the functions u and v. The Product Rule changes one variable at a time. I think my problem lies in actually finding the derivative. I need to see some more examples. I will look up some more on the internet and see if I can replicate the examples.

The substitute was a bit more confusing than the normal teacher, but I should probably watch the videos again.