Fairfield High School
AP Calculus BC
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An Explanation of Calculus and its Use
 "What in the world is Calculus?" Have you ever asked this question? For many years we heard about the impossible difficulties, and uncomprehendable concepts of Calculus. Every time we heard the name, we wondered what lay ahead of us at the end of high school and throughout college. Well, being enrolled in AP Calculus at Fairfield High School, we are being introduced into the first year of this overwhelming realm of math. On the way so far, we’ve learned a thing or two. We hope these words will clear it up a bit.    First off, no, Calculus is not the study of calculators. The term "Calculus" implies that this course is not much else than   calculating figures, or "plug-and-chug." Though many Calculus students take Calculus as purely "monkey see, monkey do"   calculating, it’s actually much more than that. Being only first year students, we can only try to shed light on the beginning   concepts of Calculus. However, since we haven’t spent too much time in Calculus, we won’t be trapped in an extremely  technical vocabulary that some more advanced Calculus students have.   Calculus is very much different from any other previous math courses. Other courses like Algebra or Geometry are mostly based on completely logical and definite bases. Though sometimes it’s easy to get lost in numbers or steps to take, the concepts weren’t too terrible. Everything is just logical numbers; that’s all it really comes down to. However, Calculus is largely based on the concept of infinity.  Obviously, its very hard to think of things as infinitely large or infinitely small. The discoverers of Calculus, however, were able to apply this concept of infinity to math. The comprehension of infinity is what makes Calculus difficult for many people, since it  is what Calculus is based on. Limits are where the concept of infinity comes into play. Limits are plainly observations as we watch a variable (x) approach a value (1, for example). For example, in the very basic graph of y=x, what happens to y as x approaches 1. y also approaches  1. This concept is applied in many places such as finding slopes at a given point of lines that aren’t straight (a process called  "differentiation" or "derivatives," to make it sound confusing), or in finding areas under curves or volumes of irregular shapes   (using something called a definite integral, again, just to intimidate people). Also using Calculus, you can graph almost any equation without having to plug it into a graphing calculator. For instance, geometry students know that the volume of a cone is  V=1/3(pi)r2h. Have you ever wondered where math wizards pull these equations from? Actually, they get it using Calculus.  They look at a cone and they slice it into circles infinitely thin. They find the areas of each slice and then using Calculus, stack them up into a volume. When they use variables, they actually get the previous formula.   This example is just one of the many examples of what Calculus is used for. Biology, Chemistry, Physics, and many other  sciences often use Calculus in comparing concentrations, finding work needed to move chains, and many other things. High   levels of Calculus are also used in engineering in things such as trying to maximize efficiency of jet fuel mixtures. Calculus is heavily used in many things today.  We know most people are convinced they will never use Calculus in their lives. Though we agree, we take it as a challenge.Even though we don’t see much use of Calculus in Medicine, Law, Journalism, and many other professions, we like to see what  technology is capable of. Every one of the students in our AP Calculus class knows how difficult Calculus is. For most of us, most of the concepts fly over our heads at super-sonic speeds. But, every once in a while, one of these concepts smacks us on the head, and, after we recover from the stun, we all "Ohhhhh!" together in understanding and awe of the power of mathematics.