Fairfield High School
AP Calculus BC
Home Page

Bibliography
Survey
Difficult Problems
Famous
Mathematicians Careers
in Math & Quotes
Logic
Problems Calc
Links Comics
Math Geek Quiz
Take the Test
Problem Responces
Sign
our Dream Book

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.