Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of calculus, states that the integral of a function over some interval can be computed by using any one of its infinitely many antiderivatives. The fundamental theorem of calculus along curves states that if has a continuous infinite integral in a region containing…
The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…
Application of Calculus in the Real World – Space Shuttle Launch Most people wonder what calculus can be used for in future career opportunities. For me this was easy to see because I knew what I wanted to go into. In the future, after college, I hope to go into the aerospace field and deal with things like planes, space shuttles and helicopters. At this point people, may not see the ridiculous amount of calculus I will use in the future, but in fact I will be using it daily. Whether it be…
subject I am seeking licensure to teach is secondary mathematics. Throughout middle school and high school, math was one of my favorite subjects. I did not enter James Madison University as a mathematics major, however, as I initially believed I wanted to teach elementary school. This was mostly because I was having difficulty deciding what subject I would teach if I chose a secondary education track. I enjoyed all of my classes in high school (except for history), and though I knew I wanted to…
While the card drawing technique is a playful method of random homework selection, it answers the call of Cooper et al. [4] in considering “non-achievement-related effects of homework” (p. 54), and more specifically addresses two contemporary important issues facing mathematics educators. The first is classroom attendance. Romer [18] discussed how absenteeism is “rampant” in undergraduate classes, adding that “steps to increase attendance, including making attendance mandatory, may deserve…
I continued on in high school with geometry, a second year of algebra, precalculus, trigonometry, and calculus. Thus far, my math courses in college have also been easy for me. My least favorite teacher was my calculus teacher, and it was not solely because of the tough subject matter. He was an engineer who took up teaching after retirement. He very simply could not teach well. He would stand in front of the board and talk through the problem at a pace that was almost impossible to follow. I…
Throughout the United States electoral votes of calculus voting is used. It is used to determine the proxy for the probability that the voter will turn out, the probability of voting, the differential benefit of one candidate winning over the other, the costs of voting, and the citizen duty. Calculus of voting is any mathematical model that predicts voting behavior by an electorate. This includes features such as participation rate. A calculus of voting represents a hypothesized decision-making…
class was enrolled in Geometry and I was behind. What confirmed it was the fact that I was the only freshman in the class. I felt discouraged because I believed that I wasn’t smart enough and I was more discouraged when I failed that year and was doomed to take the class again, much like how most of the students in “Student Fear Factor” felt. During that time, as everyone was put in Algebra II, I wanted to catch up to everyone else. Thus I enrolled in Brigham Young University’s online course for…
What is Gum Graft Surgery? What is a gum graft and why might one be needed? The initial thought of having a gum graft performed can be enough to cause some stress. However, worry not, if you need a gum graft, it is a simple procedure performed in your dentist’s office. In all honesty, it sounds worse than it actually is. If you need to have a gum graft performed, or are considering one, clearing the air of what it actually is and why it is needed may help alleviate some of your fears. A gum…
I. To begin my observation, I chose to observe Erika. I arrived after she already cleaned her unit, but I was there to see her prep her unit. She got out her instrument cassettes from the sterilizing room and her tray. Then she went to go get her patient. She was very friendly with him and asked about how his day was going so far. Erika had everything ready to go to start her patient process which looked very professional. I was also impressed with how smoothly she transitioned from asking small…