Calculus”One of the greatest contributions to modern mathematics, science, andengineering was the invention of calculus near the end of the 17th century,”says The New Book of Popular Science. Without the invention of calculus, manytechnological accomplishments, such as the landing on the moon, would have beendifficult. The word “calculus” originated from the Latin word meaning pebble. This isprobably because people many years ago used pebbles to count and do arithmeticproblems. The two people with an enormous contribution to the discovery of thetheorems of calculus were Sir Isaac Newton of England and Baron GottfriedWilhelm of Germany. They discovered these theorems during the 17th centurywithin a few years of each other.
Isaac Newton was considered one of the great physicists all time. Heapplied calculus to his theories of motion and gravitational pull. He was ableto discover a function and describe mathematically the motion of all objects inthe universe. Calculus was invented to help solve problems dealing with “changing orvarying” quantities. Calculus is considered “mathematics of change.
” There aresome basic or general parts of calculus. Some of these are functions,derivative, antiderivatives, sequences, integral functions, and multivariatecalculus. Some believe that calculus is too hard or impossible to learn without muchmemorization but if you think that calculus is all memorizing then you will notget the object of learning calculus. People say that calculus is just therevision or expansion of old or basic equations and I believe that also.
In economics and business there are some uses for calculus. One importantapplication of integral calculus in business is the evaluation of the area undera function. This can be used in a probability model. Probability is anotheruses in integral calculus for business because you could find how oftensomething will appear in a certain range in a certain time. A function used forprobability in uniform distribution.
The function is f(x) = 1 (b – a) for a = b. Some economics uses is figuring marginal and total cost. The functionis TC = MC = TVC + FC. Another is the demand on a sales product. ex.
Demand onBeer 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 = averageretail price of beer r = average retail price level of all other consumer goodss = measure of strength of beer (how consumers like it) as you can see ifeverything but r stays constant then the demand will go up. Some terms used in calculus frequently used to learn you need to know whatthey are. Derivative is the fundamental concept of calculus that is how thingschange. (ex.
instantaneous velocity) Functions are always used in allapplications. A function is an equation with one or more variables where onlyone x value will produce only one y value is a function. Also you will need tolearn and memorize some theorems and identities to be able to expand andbreakdown equations. THE NEW BOOK OF POPULAR SCIENCECalculus p.
431 – 433 Brief Calculus and its ApplicationsLarry J. Goldstein / David C. Lay / David L. Schneider McGraw Hill Encyclopediaof Science and Technology #3 ed. 7A First Course in Calculus Lang, Serge Addison-Wesley Publishing CompanyCalculus for Business and Economics Childress, Robert L.
Prentice Hall inc.Englewood Cliffs, New Jersey