Calculus

"One of the greatest contributions to modern mathematics, science, and engineering was

the invention of calculus near the end of the 17th century," says The New Book of Popular

Science. Without the invention of calculus, many technological accomplishments, such as the

landing on the moon, would have been difficult.

The word "calculus" originated from the Latin word meaning pebble. This is probably

because people many years ago used pebbles to count and do arithmetic problems.

The two people with an enormous contribution to the discovery of the theorems of

calculus were Sir Isaac Newton of England and Baron Gottfried Wilhelm of Germany. They

discovered these theorems during the 17th century within a few years of each other.

Isaac Newton was considered one of the great physicists all time. He applied calculus to

his theories of motion and gravitational pull. He was able to discover a function and

describe mathematically the motion of all objects in the universe.

Calculus was invented to help solve problems dealing with "changing or

varying" quantities. Calculus is considered "mathematics of change."

There are some basic or general parts of calculus. Some of these are functions,

derivative, antiderivatives, sequences, integral functions, and multivariate calculus.

Some believe that calculus is too hard or impossible to learn without much memorization

but if you think that calculus is all memorizing then you will not get the object of learning

calculus. People say that calculus is just the revision or expansion of old or basic equations and I

believe that also.

In economics and business there are some uses for calculus. One important application of

integral calculus in business is the evaluation of the area under a function. This can be used

in a probability model. Probability is another uses in integral calculus for business because you

could find how often something will appear in a certain range in a certain time. A function used

for probability in uniform distribution. The function is f(x) = 1 \ (b - a) for a < x >= b. Some

economics uses is figuring marginal and total cost. The function is TC = {MC = TVC + FC.

Another is the demand on a sales product. ex. Demand on Beer that brings in different variables

to see how the consumption of beer is. The function is a multivariate function f(m, p, r, s) =

(1.058)(m^.136)(p^-.727)(r^.914)(s^.816) where

m = aggregate real income : p = average retail price of beer

r = average retail price level of all other consumer goods

s = measure of strength of beer (how consumers like it)

as you can see if everything but r stays constant then the demand will go up.

Some terms used in calculus frequently used to learn you need to know what they are.

Derivative is the fundamental concept of calculus that is how things change. (ex. instantaneous

velocity) Functions are always used in all applications. A function is an equation with one or

more variables where only one x value will produce only one y value is a function. Also you

will need to learn and memorize some theorems and identities to be able to expand and breakdown

equations.