Well the prompt asks about inductive vs deductive learning, and I don't know what either means, so I'm going to have to look it up.
Well I'm back. Based on what what I've read, I would say this theorem is more inductive. Basically, it doesn't matter how well it is explained; you still might not get it. You basically just have to keep trying and using calc and eventually it will click and it will make sense why it works. For me, the moment when it all kinda clicked was in the shower. No joke. I don't think I was even thinking about math, but somehow it just clicked, and it made sense why the inverse derivative of an original function was the area of it, and why we use integrals. I would say its fundamental, because half of everything calculus does is based of it (assuming calc is half derivative and have integral stuff). The notation is simple enough and makes sense. One thing I don't really get is how it relates to infinite rectangles. That seems completely unrelated to the integrals to me.
0 Comments
We'll its been a while since we've done blog posts so we've learned quite a bit since the last blog. The main thing we've been doing recently is definite integrals. Before we did that, we did the whole concept of using rectangles to find the area under the curve of a function. Using more rectangles is more accurate (obviously). To get a perfect area you'd want to use infinite rectangles, so that's were limits come in. There's this long sum notation thing that equals the integral notation. We did a big long proof which was kind of confusing but kind of made sense. We then learned how to actually solve define integrals by hand which luckily was much easier then the crazy proof. As of right now, I can do all the things we've done so far but I don't completely understand it. I'm basically just following the steps. I don't get how the inverse derivative relates to having infinite amount of rectangles. But I'm pretty sure it will click more as we do it more, which is what usually happens in math if it doesn't make complete sense at first.
|
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
January 2018
Categories |