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.
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February 2015
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