Calculus

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    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…

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    Ap Calculus Challenges

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    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…

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    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.…

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    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…

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    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…

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    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…

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    Coaching Math

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    Math is an exact science; there is no grey location. Much like another location to look at, we need to first analyze the basics to head farther. Even artwork requires a basic knowledge of paints, brushes, backgrounds, expression, composition, and plenty greater. Very not often can a person just make it up to get the meaning of it. The identical is going for math. Very hardly ever are you able to just make something up, “guess,” and get by. However, coaching math is one hassle in itself. We first…

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    While all the other children cried about the math saying it was too hard or boring I on the other hand enjoyed it. This followed me to high school and even then nothing changed. Not even the crying everyone still fell over at the site of a big math formula or equation. But it wasn’t until my junior year of high school when I met my physics teacher who is still my mentor to this day. He truly showed me the wonders and joy that math could offer. We taught me more than I could have ever imagine. We…

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    I love challenging myself, to test my own limit. Therefore during my Sophomore year, I decided to take Pre-Calculus and AP Calculus at the same time. This was quite a bold move for myself, due to the fact that I would have to learn Pre-Calculus on my own in order to pass the class, and I was not a very good math student to start with. Both my Pre-Calculus teacher, and my Calculus teacher tried to discourage me from doing that. However, I was ready for the challenge and I was determined to make…

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    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…

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