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 = 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.

THE NEW BOOK OF POPULAR SCIENCE

Calculus p.431 – 433 Brief Calculus and its Applications

Larry J. Goldstein / David C. Lay / David L. Schneider McGraw Hill Encyclopedia

of Science and Technology #3 ed. 7

A First Course in Calculus Lang, Serge Addison-Wesley Publishing Company

Calculus for Business and Economics Childress, Robert L. Prentice Hall inc.

Englewood Cliffs, New Jersey