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.…
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…
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…
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…
He helped developed differential and integrals calculus along with Newton. Leibniz was born on july 1st 1646. He was the one who discovered the coefficients of systems of linear equations. Leibniz also has a important formula for pi. The formula concludes that 1 - ⅓ +⅕ - 1/7 + = Pi/4. Leibniz was so smart and discovered many thing. He was known to be the first computer scientist due to his binary numeral system. Besides the main founders there are also some not as famous people who helped find…
After the first import of mathematical ideas from the 6th century (Smith), there was no established notation for mathematics until Seki Takakazu (関 孝和) and his followers did so in the 17th century (Deal, Mathematics). As the Japanese language is written vertically from right to left, as opposed to horizontally from left to right, the resulting notation was very different to its western equivalents. The other prime example is enri. Similar to its western counterpart of calculus, this branch of…
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…