Docstoc

Calculus

Document Sample
Calculus Powered By Docstoc
					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.

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