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…
One challenge I've experienced during my pursuit in engineering and my education as a whole has been AP Calculus AB. Considering I've had high grades in previous maths, I assumed that calculus would not be a problem. However, those previous classes could not have given me a sense of what a college level math class would be like, which I learned very quickly. Calculus has been a surprising taste of what college learning is like. I now know that much of the learning is going to be one's own…
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.…
The most challenging course which I excelled in would be Pre-Calculus. Throughout my middle school and high school years math has always been my favorite subject. Math has always come to me as second nature. From the beginning of my junior year in high school I was taking duel enrollment pre-calculus. However, with problems with lacking paper work I was pulled out of the class and had to take a regular pre-ap pre-calculus class. The problem was that everyone else in that class was all ahead of…
Calculus was by far my hardest class during my senior year. During this year I felt that all my other classes got easier, except from math. I got a sense that I was going to breeze by senior year and so my work ethic dropped tremendously. However, I still knew I couldn’t let my grades drop for the first semester of senior year and I was able to get a B. After first semester, my other classes got even easier but math kept getting harder and my work ethic kept dropping. I was already accepted into…
Another class that is helping me grow as a student through skills for academic success is AP Calculus. I’ve always been sort of good at math but this class was nothing I had expected it to be. Typically, in math you learn the rule or the formula and then you just use it straightforward. Calculus is anything but straightforward. In this class you learn the rule and formula but you are expected to figure out how to use them in a number of different ways. Other math classes have been tests of…
Approaching junior year, I remained uncertain regarding my upcoming course choices. I had taken Math III during the previous semester and felt confident in my math abilities when reflecting upon the course. I knew I needed one more math credit, but I did not know if I should sign up for Honors Discrete Mathematics or Honors Precalculus. Knowing I would face a Calculus class while in college, I decided to take Honors Precalculus, not knowing the challenge that awaited me. Consequently, I…
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…
junior, I doubled up on math courses by taking Pre-Calculus and AP Calculus BC at the same time. Even though I didn’t know if I could handle it, I signed up for it because that was what students who were good at math did. Taking classes that everyone else was taking was how I chose my classes. I did well in all of my classes, but I was not genuinely interested in any of them; so, I never had any preference in the classes I take. Three short weeks into September, I had my first test in my…
When I first began this school year, I never thought that I’d learn this much about calculus at only one quarter in. Even at a couple of weeks in, when the class was reviewing what we’ve already learned, there were some things that I had to learn because I’ve never seen them before. Looking back, I’d say that my work ethic has also definitely improved along with my learning skills. Now not only am I learning better in calculus, but also in my other classes as well. In this class, there are…