This week in AP Calculus, we learned more about u-substitutions, integrals, and slope fields. This is important because all of these concepts can be tied together. By looking at derivatives and anti-derivatives, we can determine slope and original functions. To evaluate an integral, you can use u-substitution. We learned a little bit about u-substitution at the beginning of the year. We have also determined slope from the derivative previously. Like I said before, these concepts all tie together, and we are just taking a more in-depth look at them. I understood slope fields very well this week. Since using derivatives to determine slope is fresh in my mind, I was able to understand these extremely well. I did not really struggle because these concepts are pretty familiar to me. To determine slope field, what you do is you take a point on the dot paper and plug it into the derivative. If the point we are looking at is (1,1), we would plug in 1 for x and 1 for y, solve the equation, and make a mark on the dot of the number/slope we get. Once the entire field has a mark, the result is the slope field. My participation was very solid this week. All I really have to do is prepare for the upcoming test next week.
This week, we learned about the fundamental theorem of calculus. In my experience, deductive learning really helped solidify the concepts for me. Inductive learning was what let me discover the topics, but deductive learning told me why those things were true. Combining the two methods of learning was helpful, because it went from discovery learning to analytic learning. The two together helped with complete understanding of the concepts. The fundamental theorem of calculus is very fundamental, because it is the basis for a lot of the calculus we have been doing and will be doing. We can describe a lot of things we haven't been able to in the past. Once we understand the theorem, it will also allow us to understand previous topics and upcoming topics better. The theorem shows us the net area of a graph. This can describe the behavior and relationships that graphs share. It will help us learn more about a graph. We will think of graphs as more than just lines, and we will be able to describe them better. Using a combination of all the concepts in calculus and the fundamental theorem, we will be able to understand equations and graphs at a higher level.
This week in AP Calculus, we continued learning about how to calculate the area under the curves of functions. We got much more in-depth this week, since we had only just begun learning about this topic before break. We also learned about how to calculate the definite integrals using antiderivatives. This was taught by hand and in our calculators. Before, we had to draw the function ourselves, and look at the graph to figure out the problem. This process became much easier by learning these alternative methods. This will help us calculate area under curves much easier. The lessons we learned this week finished off the sections, so now we have to study for the upcoming test. I understood pretty much everything this week. I didn't really struggle at all, but I have to look over the chapter and study for the upcoming tests. To calculate an integral using antiderivatives, you calculate the antiderivative. You can calculate the antiderivative of something by adding one to the exponent and then dividing the whole term by the exponent you get. Then, you plug in the intervals and subtract, multiplying by the interval. My participation was miraculous this week. I still need to prepare for the test next week.
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February 2015
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